tag:blogger.com,1999:blog-73669402784184247972017-08-17T07:04:27.304-04:00Engaging MathPosting engaging activities for grade 7-12 mathDavid Petronoreply@blogger.comBlogger63125tag:blogger.com,1999:blog-7366940278418424797.post-62466763495407382042017-06-30T13:43:00.000-04:002017-06-30T13:43:36.836-04:00Trig Identities Continuum<div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EwAq7Yvmj89U7DkCmICFIdQCPcBGAYYCw/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="99" data-original-width="957" height="33" src="https://2.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EwAq7Yvmj89U7DkCmICFIdQCPcBGAYYCw/s320/EM_Activity.png" width="320" /></a></div><a href="https://4.bp.blogspot.com/-UxQ4T931ArU/WVQDvKTiIZI/AAAAAAAACqQ/XUMITRfzN7Q986gX23SCP8RZubPjmxovgCLcBGAs/s1600/TrigIdentityContinuum.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1280" data-original-width="1280" height="320" src="https://4.bp.blogspot.com/-UxQ4T931ArU/WVQDvKTiIZI/AAAAAAAACqQ/XUMITRfzN7Q986gX23SCP8RZubPjmxovgCLcBGAs/s320/TrigIdentityContinuum.JPG" width="320" /></a>We have started to develop a number of "<a href="http://engaging-math.blogspot.ca/search/label/continuum" target="_blank">Continuum</a>" activities. In these activities, students are given basic knowledge questions on cards from an envelope. On each card there is one type of question. When the student completes a set number of questions on their card correctly, then they replace that card and grab a new card from the next envelope. This next envelop will typically have problems of a similar (to each other) type but incrementally more difficult than the previous envelope. In this way students move from simpler to more difficult questions at their own pace. The cards start with Quotient and Reciprocal Identities, then move to Pythagorean, then to progressively more difficult mixed identities and finally a card where they make their own.<br /><br /><a href="https://4.bp.blogspot.com/-dalca0OinTo/WPlRJfEuVlI/AAAAAAAACfU/CWt6daQ6c7IWRRCf_RXplYNgf0MIhdWVgCPcBGAYYCw/s1600/FractionInk.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="360" data-original-width="576" height="125" src="https://4.bp.blogspot.com/-dalca0OinTo/WPlRJfEuVlI/AAAAAAAACfU/CWt6daQ6c7IWRRCf_RXplYNgf0MIhdWVgCPcBGAYYCw/s200/FractionInk.gif" width="200" /></a>We've created two versions. One where all the equations are identities and one where some of them are not. Typically when we have done these, students could check their answers by using a UV pen to reveal the answers written on the answer cards (see example from our <a href="http://engaging-math.blogspot.ca/2017/04/fraction-operation-continuum.html" target="_blank">fraction continuum</a> to the right). Because these are identities we chose to have the two sets so if you use set one, students just verify that they are identities. However, if you use set two, students will have to figure out which ones are and which are not identities. So on this second set you could have cards that have the invisible ink that verify which are the identities. <br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://3.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAKlet-tqOf56HLz_d2gXQpwCPcBGAYYCw/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="99" data-original-width="957" height="33" src="https://3.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAKlet-tqOf56HLz_d2gXQpwCPcBGAYYCw/s320/EM_Curriculum.png" width="320" /></a></div><br /><ul><li>MCR3U - 1.5 prove simple trigonometric identities, using the Pythagorean identity sin<sup>2</sup>(x) + cos<sup>2</sup>(x) = 1;&nbsp;the quotient identity tan(x) = sin(x)/cos(x); and the reciprocal identities sec(x) = 1/cos(x), csc(x) = 1/sin(x) , and cot(x) = 1/tan(x)</li><li>MHF4U - As review</li></ul><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFrakRNaLclhQ2xdx_irLtfapAACPcBGAYYCw/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="99" data-original-width="957" height="33" src="https://2.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFrakRNaLclhQ2xdx_irLtfapAACPcBGAYYCw/s320/EM_Materials.png" width="320" /></a></div><ul style="background-color: white; color: #6a6a6a; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 1.4; list-style-image: initial; list-style-position: initial; margin: 0.5em 0px; padding: 0px 2.5em;"><a href="https://2.bp.blogspot.com/-n04bev-yfLQ/WVZ1NtRx2hI/AAAAAAAACq4/BZLbDCcw9c8q3KhsDDcfIxOPC-6pOax7QCLcBGAs/s1600/TrigContinuum1.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1278" data-original-width="982" height="320" src="https://2.bp.blogspot.com/-n04bev-yfLQ/WVZ1NtRx2hI/AAAAAAAACq4/BZLbDCcw9c8q3KhsDDcfIxOPC-6pOax7QCLcBGAs/s320/TrigContinuum1.png" width="244" /></a><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">Enough copies of each of the question cards for your class (there are six cards per page at each level) in different colour card stock for each level, laminated (use colours that allow seeing the magic pen writing - you may want to test this). You will likely not need as many cards in the last few envelopes as students work at different paces.&nbsp;</li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">If you are using the set with the non-identities then you should have 3 sets of the answer cards (use magic pen to write the answers anywhere along each equation - the answers are on the last page of the Google Doc). The answer cards are the same as the question cards but you write the answers in invisible ink on them. To help distinguish the answer cards to the question cards you should put a stamp or sticker on the back. Write on the cards first then laminate them. If you write on the card after lamination then the ink tends to wear off. There are sample solutions at the end of each document. That is for you to carry around (or not) but not for showing students but more for your reference.</li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">3 "magic" pens can be purchased at&nbsp;<a href="https://www.chapters.indigo.ca/en-ca/paper/secret-message-writing-set/5037200004502-item.html?ikwid=secret+message+writing&amp;ikwsec=Home&amp;ikwidx=0" style="color: #7ba2d3; text-decoration-line: none;" target="_blank">Chapters/Indigo</a>&nbsp;or we found these at a Scholastic's book fair. We have since purchased some on&nbsp;<a href="http://www.ebay.ca/sch/i.html?_odkw=uv+pen&amp;_osacat=0&amp;_from=R40&amp;_trksid=p2045573.m570.l1313.TR0.TRC0.H0.Xuv+invisible+pen.TRS0&amp;_nkw=uv+invisible+pen&amp;_sacat=0" style="color: #7ba2d3; text-decoration-line: none;" target="_blank">eBay</a>&nbsp;or&nbsp;<a href="https://www.amazon.ca/s/ref=nb_sb_noss_1?url=search-alias%3Daps&amp;field-keywords=invisible+ink+pen&amp;rh=i%3Aaps%2Ck%3Ainvisible+ink+pen" style="color: #7ba2d3; text-decoration-line: none;" target="_blank">Amazon</a>.</li></ul><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-lGro3asxop4/VUj5VAiy0HI/AAAAAAAAAj4/Em1wzntOFOUw0v1ap3GTkFmpT-BUYKdWACPcBGAYYCw/s1600/UVpens.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="261" data-original-width="1000" height="103" src="https://1.bp.blogspot.com/-lGro3asxop4/VUj5VAiy0HI/AAAAAAAAAj4/Em1wzntOFOUw0v1ap3GTkFmpT-BUYKdWACPcBGAYYCw/s400/UVpens.png" width="400" /></a></div><div><span style="color: #6a6a6a; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><span style="font-size: 14.85px;"><br /></span></span></div><div class="separator" style="clear: both; text-align: left;"><a href="https://3.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cuWWsgsFafGrCMylZCgIVNwCPcBGAYYCw/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="99" data-original-width="957" height="33" src="https://3.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cuWWsgsFafGrCMylZCgIVNwCPcBGAYYCw/s320/EM_Procedure.png" width="320" /></a></div><a href="https://4.bp.blogspot.com/-0iYJnlOILzg/WVaLm9H7MeI/AAAAAAAACrI/52JC0_2J4jcvbwqFdYXoYMmvfb-yiSyqACLcBGAs/s1600/Envelopes.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="456" data-original-width="466" height="195" src="https://4.bp.blogspot.com/-0iYJnlOILzg/WVaLm9H7MeI/AAAAAAAACrI/52JC0_2J4jcvbwqFdYXoYMmvfb-yiSyqACLcBGAs/s200/Envelopes.png" width="200" /></a><br /><ol><li>Place the questions in piles (or in envelopes taped to the wall) in order of difficulty and set up three stations for the answer cards (if you are using the ones with non-identities). Students will get a card and answer the first 4 questions.&nbsp;</li><li>Normally we might have students start at different places but because of the fact that there are different identities on each card, students should start at the first envelope. &nbsp;</li><li>If they are using the set with non-identities, to check their answers, they will go to a station and use the magic pens. Students may decide to do one question at a time and then go check their answer or they may do all 4 and then check. Students are monitoring themselves so they decide. If they get the first 4 right, they have a level of mastery to move themselves to the next card. If not there are more questions on the card until they master that type. You can decide whether you want them to do the other 4 or just do enough to get a total of four correct.&nbsp;</li><li>As they move through the continuum, the hope is that they reach level 4 which matches the grade 11 curriculum. You may wish to have them do all the questions on that card.&nbsp;</li><li>The fifth level is set up to challenge students who are moving forward quickly. Here they create their own question.</li></ol><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6EcRSdZHbykpxMl1n8JcBd5wCPcBGAYYCw/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="99" data-original-width="957" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6EcRSdZHbykpxMl1n8JcBd5wCPcBGAYYCw/s320/EM_Downloads.png" width="320" /></a></div>Note that we have been having some issues with Google Docs reformatting the cards depending on what machine or browser you are using. So you may have to reformat when you make your own copy. For a good version, just use the PDFs.<br /><br /><ul><li>Gr 11 Trig Identities Continuum &nbsp;<a href="https://drive.google.com/open?id=1f-IZdMrup6G3yiKwFQ5ej0OYxRwbNbyXGRCBYVYIVZ8" target="_blank">Google Doc</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkamoyMVVEaFp4NWc" target="_blank">PDF</a></li><li>Gr 11 Trig Identities Continuum (with non-identities) <a href="https://drive.google.com/open?id=1hQ7GzPoMpQZR-UGIqqxsWc3sfY2BIt9u9Y8Vr9CX3MQ" target="_blank">Google Doc</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkUG5pRkFwMzJQWFk" target="_blank">PDF</a></li></ul><br /><span style="background-color: white; color: #6a6a6a; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 15px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span><br />David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-1394108536284452212017-04-26T13:39:00.000-04:002017-04-26T15:57:46.381-04:00Sort Students into Groups using Percents, Fractions and Decimals<br /><a href="http://3.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" width="320" /></a><br /><a href="http://2.bp.blogspot.com/-YXmU1x0LFdc/WQDUjodt1dI/AAAAAAAAAeY/8yB3QovzYtohe7B2ri0UyTwBz5r1TYAbQCK4B/s1600/ScreenHunter_08%2BApr.%2B26%2B13.00.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="269" src="https://2.bp.blogspot.com/-YXmU1x0LFdc/WQDUjodt1dI/AAAAAAAAAeY/8yB3QovzYtohe7B2ri0UyTwBz5r1TYAbQCK4B/s320/ScreenHunter_08%2BApr.%2B26%2B13.00.jpg" width="320" /></a>I<span style="font-family: inherit;">n this activity students are each given one card.&nbsp;The&nbsp;card&nbsp;will either have a fraction, percent or decimal. Their job is to find the two other students&nbsp;who have the same value but a different representation. This shouldn't take too long and&nbsp;could be repeated every couple of days just to solidify conversion between fraction, decimal and percent</span>.<br /><br />If you wish you can also have students do this individually with this Desmos <a href="https://teacher.desmos.com/activitybuilder/custom/5900f76cadd3150616108044" target="_blank">cardsort</a>.<br /><br /><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" width="320" /></a><br /><ul><li><span style="font-family: inherit;">Gr7 - determine, through investigation, the relationships among fractions, decimals, percents, and ratios</span></li><li><span style="font-family: inherit;">Gr8 - translate between equivalent forms of a number (i.e., decimals, fractions, percents)</span></li><li><span style="font-family: inherit;">MPM1D, MFM1P - As review</span></li></ul><div><a href="http://1.bp.blogspot.com/-WTVjtoXVvKw/WQDJE0_P4-I/AAAAAAAAAd4/NYNUzVFJxv0H_eM8OZahbNUmxjwaRm13wCK4B/s1600/ScreenHunter_07%2BApr.%2B26%2B12.18.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="160" src="https://1.bp.blogspot.com/-WTVjtoXVvKw/WQDJE0_P4-I/AAAAAAAAAd4/NYNUzVFJxv0H_eM8OZahbNUmxjwaRm13wCK4B/s200/ScreenHunter_07%2BApr.%2B26%2B12.18.jpg" width="200" /></a><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" width="320" /></a></div><div><ul><li>Download the cards and cut them out (you may want to put them on cardstock and laminate)</li></ul><div><br /></div><div><br /></div><div></div></div><div><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" width="320" /></a></div><div><ol><a href="http://3.bp.blogspot.com/-S_-CqME8WG8/WQDIy0eF9TI/AAAAAAAAAdw/jNdmzkCcaNsxabh9b2fvSjcVa4IigN4YgCK4B/s1600/ScreenHunter_06%2BApr.%2B26%2B12.16.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="157" src="https://3.bp.blogspot.com/-S_-CqME8WG8/WQDIy0eF9TI/AAAAAAAAAdw/jNdmzkCcaNsxabh9b2fvSjcVa4IigN4YgCK4B/s200/ScreenHunter_06%2BApr.%2B26%2B12.16.jpg" width="200" /></a><li>Shuffle the cards and distribute one per student. Note that there are 12 sets of 3 cards so you may want to remove sets to more closely match your student population.&nbsp;</li><li>Instruct students to find the two other people that have the same value but a different representation.&nbsp;</li><li>Once students find their partners they will be in groups of three,</li></ol><div><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" width="320" /></a></div><div><div><ul style="background-color: white; color: #6a6a6a; font-size: 14.85px; line-height: 20.79px; margin: 0.5em 0px; padding: 0px 2.5em;"><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;"><span style="font-family: inherit;">Group Fractions, Decimals, Percent Cards (<a href="https://drive.google.com/open?id=1_UJeDMVvjobnIZ8QKH_9-sv0RhTWyPtNC1olQED1QCs" target="_blank">Googledoc</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkdDFJNGFVaWRGd0U" target="_blank">pdf</a>)</span></li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;"><span style="font-family: inherit;">Individual Desmos Cardsort <a href="https://teacher.desmos.com/activitybuilder/custom/5900f76cadd3150616108044" target="_blank">Version</a></span></li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;"></span><span style="background-color: white; color: #6a6a6a; font-family: inherit; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span></div></div><div></div></div>GISELE JOBINhttps://plus.google.com/115554386495766205389noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-69805833697170546622017-04-20T21:23:00.001-04:002017-04-22T19:37:40.942-04:00Fraction Operation Continuum <div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EOtR_fu1wjGcRR5kJ3oShmwCPcB/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EOtR_fu1wjGcRR5kJ3oShmwCPcB/s320/EM_Activity.png" width="320" /></a></div><a href="http://2.bp.blogspot.com/-WZl0zBBOdwE/WPkj6SyRjjI/AAAAAAAACfE/JPcOXx6yo1w2tIkIt_d_KlHp81cPsH3vACK4B/s1600/IMG_3178.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="240" src="https://2.bp.blogspot.com/-WZl0zBBOdwE/WPkj6SyRjjI/AAAAAAAACfE/JPcOXx6yo1w2tIkIt_d_KlHp81cPsH3vACK4B/s320/IMG_3178.JPG" width="320" /></a>As math teachers we definitely want our students to practice to become proficient but piles of problems or worksheets aren't going to be very engaging to students. We think this tweak to the standard worksheet is a way to turn those boring questions into something more engaging.<br /><br />In Ontario, grade 7s are introduced to operations with fractions. Addition &amp; subtraction and multiplication &amp; division with whole numbers. The premiss here is fairly simple. Students are presented with multiple cards of questions (in this case of adding and subtraction of fractions (with a little of division and multiplication with whole numbers). The cards represent problems that increase in difficulty as you go from one to the next. Students can all start at the first envelope or you could give them an exit card the day before to help place them in a particular card to start. Students check their own answers using answer cards with the answers written with "invisible" ink that can be revealed by shining a UV light on it.<br /><br />Students really seem to like this style of activity as they feel empowered to move from card to card when they are ready and the added feature of checking the answers with the UV pen gives a sense of novelty. This could be used as practice or review.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-dalca0OinTo/WPlRJfEuVlI/AAAAAAAACfQ/mOv1aL_st2AckdQlSCnZofQbjKBSjOWrACLcB/s1600/FractionInk.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-dalca0OinTo/WPlRJfEuVlI/AAAAAAAACfQ/mOv1aL_st2AckdQlSCnZofQbjKBSjOWrACLcB/s320/FractionInk.gif" width="560" /></a></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAglEYBLiwXpC3aBc223OTxwCPcB/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAglEYBLiwXpC3aBc223OTxwCPcB/s320/EM_Curriculum.png" width="320" /></a></div><ul><a href="https://3.bp.blogspot.com/-LbZHMe4ANdY/WPlZnCjiB1I/AAAAAAAACfw/OFSFvQJRLoAsJ1xuuzRAOgcDwEqtoL4BACLcB/s1600/IMG_3189.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://3.bp.blogspot.com/-LbZHMe4ANdY/WPlZnCjiB1I/AAAAAAAACfw/OFSFvQJRLoAsJ1xuuzRAOgcDwEqtoL4BACLcB/s200/IMG_3189.JPG" width="200" /></a><li>Gr7 -&nbsp;divide whole numbers by simple fractions</li><li>Gr7 - use a variety of mental strategies to solve problems involving the addition and subtraction of fractions</li><li>Gr7 -&nbsp;add and subtract fractions with simple like and unlike denominators, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, calculators) and algorithms;</li><li>Gr7 -&nbsp;&nbsp;demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number</li><li>Gr8 - As review (we plan an extension so that this could be used for grade 8 with multiplying and dividing fractions)</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://3.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFraklMQHtndVskF77GmYhgGDGwCPcB/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFraklMQHtndVskF77GmYhgGDGwCPcB/s320/EM_Materials.png" width="320" /></a></div><ul><a href="https://2.bp.blogspot.com/-nvqlNWh1rLY/WPlYTQDF26I/AAAAAAAACfg/uI9UoXMYhAYgkbOZvcUjYVC4owDLhDmAQCLcB/s1600/Screen%2BShot%2B2017-04-20%2Bat%2B2.47.08%2BPM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="248" src="https://2.bp.blogspot.com/-nvqlNWh1rLY/WPlYTQDF26I/AAAAAAAACfg/uI9UoXMYhAYgkbOZvcUjYVC4owDLhDmAQCLcB/s320/Screen%2BShot%2B2017-04-20%2Bat%2B2.47.08%2BPM.png" style="cursor: move;" width="320" /></a><li>Enough copies of each of the question cards for your class (there are four cards per page at each level) in different colour card stock for each level, &nbsp;laminated (use colours that allow seeing the magic pen writing - you may want to test this). You will likely not need as many cards in the last few envelopes as students work at different paces. You will need as many as you have in your class if you decide to start everyone at the first level. Fewer if you let students start at different levels (see below)</li><li>3 sets of the answer cards (use magic pen to write the answers anywhere along each equation, they could be sideways, upside-down, (the answers are on the last page of the Google Doc). The answer cards are the same as the question cards but you write the answers in invisible ink on them. To help distinguish the answer cards to the question cards you should put a stamp or sticker on the back. Write on the cards first then laminate them. If you write on the card after lamination then the ink tends to wear off. There is a separate answer card on the last page of the download. That is for you to carry around (or not) but not for showing students but more for your reference.</li><li>3 "magic" pens can be purchased at <a href="https://www.chapters.indigo.ca/en-ca/paper/secret-message-writing-set/5037200004502-item.html?ikwid=secret+message+writing&amp;ikwsec=Home&amp;ikwidx=0" target="_blank">Chapters/Indigo</a> or we found these at a Scholastic's book fair. We have since purchased some on <a href="http://www.ebay.ca/sch/i.html?_odkw=uv+pen&amp;_osacat=0&amp;_from=R40&amp;_trksid=p2045573.m570.l1313.TR0.TRC0.H0.Xuv+invisible+pen.TRS0&amp;_nkw=uv+invisible+pen&amp;_sacat=0" target="_blank">eBay</a> or <a href="https://www.amazon.ca/s/ref=nb_sb_noss_1?url=search-alias%3Daps&amp;field-keywords=invisible+ink+pen&amp;rh=i%3Aaps%2Ck%3Ainvisible+ink+pen" target="_blank">Amazon</a>.</li></ul><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-lGro3asxop4/VUj5VAiy0HI/AAAAAAAAAj4/dBAlRjl21SQocxZZq62H0SMqjRwvCEHhw/s320/UVpens.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-lGro3asxop4/VUj5VAiy0HI/AAAAAAAAAj4/dBAlRjl21SQocxZZq62H0SMqjRwvCEHhw/s320/UVpens.png" width="560" /></a></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cpagYRup3TCO3EN4S8OgGzACPcB/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cpagYRup3TCO3EN4S8OgGzACPcB/s320/EM_Procedure.png" width="320" /></a></div><ol><li>Place the questions in piles (or in envelopes taped to the wall) in order of difficulty and set up three stations for the answer cards. Students will get a card and answer the first 5 questions.&nbsp;<div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-mlF22WcphuA/WPlZIYx10kI/AAAAAAAACfo/fFgFVbjonQAvjWIjyUNSbV0lUyc8tFW2gCLcB/s1600/IMG_3179.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-mlF22WcphuA/WPlZIYx10kI/AAAAAAAACfo/fFgFVbjonQAvjWIjyUNSbV0lUyc8tFW2gCLcB/s320/IMG_3179.JPG" width="560" /></a></div></li><li>You could have all students start at level 1 but for this activity to be most successful, students should start at the appropriate envelope. If they start in one that is too hard they will be frustrated and if they start in one that is too easy they will be bored. Use an exit card (the day before) to help you decide which envelope each student should start in. When given back the exit card write down the level they will start in.&nbsp;</li><li>To check their answers, they will go to a station and use the magic pens. Students may decide to do one question at a time and then go check their answer or they may do all 5 and then check. Students are monitoring themselves so they decide. If they get the first 5 right, they have a level of mastery to move themselves to the next card. If not there are more questions on the card until they master that type. You can decide whether you want them to do the other 5 or just do enough to get a total of five correct.&nbsp;</li><li>As they move through the continuum, the hope is that they reach level 6 which matches the grade 7 curriculum. Since our goal is to get them to level 6, students should solve ALL equations on that card instead of just five.&nbsp;</li><li>The seventh level is set up to challenge students who are moving forward quickly. They should solve all questions on this card. &nbsp;</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-fu1K4ukRHVA/U615osjMAPI/AAAAAAAAAE8/2esFrIbsemgrzfZWLwr4zDvSSm6jEM8BgCPcB/s1600/EM_SampleWork.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-fu1K4ukRHVA/U615osjMAPI/AAAAAAAAAE8/2esFrIbsemgrzfZWLwr4zDvSSm6jEM8BgCPcB/s320/EM_SampleWork.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div><div style="text-align: center;"><iframe allowfullscreen="true" frameborder="0" height="389" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1v2gbGPa88T7k6PmVgaZqGd-GKD6gIuhVTaOy82Nujd4/embed?start=true&amp;loop=true&amp;delayms=5000" webkitallowfullscreen="true" width="480"></iframe></div></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://3.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6E-q1VkeGwQKEH9LGbINliCgCPcB/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6E-q1VkeGwQKEH9LGbINliCgCPcB/s320/EM_Downloads.png" width="320" /></a></div><ul><li>Fraction Operation Continuum (with Answers) - (<a href="https://drive.google.com/open?id=0B9algQOOR_bkX2dSN2pCTnRobjA" target="_blank">PDF</a>, <a href="https://drive.google.com/open?id=1vjL75mBKtz9bpcT-TalcT6AlSjB0MllSAEpPrlOu0hI" target="_blank">Google Doc</a>)</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-39134612187171520462017-02-24T13:53:00.003-05:002017-03-20T14:12:51.793-04:00Investigating Graphs of Rational Functions<div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EOtR_fu1wjGcRR5kJ3oShmwCPcB/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EOtR_fu1wjGcRR5kJ3oShmwCPcB/s320/EM_Activity.png" width="320" /></a></div><a href="https://1.bp.blogspot.com/-jNKJHcNTYx8/WFg9Cie6feI/AAAAAAAABpw/z5ZUlzB0Z7oxInYA9N1Ynsq1YvpQDz-twCLcB/s1600/RationalFunctionsCardsort.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://1.bp.blogspot.com/-jNKJHcNTYx8/WFg9Cie6feI/AAAAAAAABpw/z5ZUlzB0Z7oxInYA9N1Ynsq1YvpQDz-twCLcB/s200/RationalFunctionsCardsort.JPG" width="200" /></a>In Ontario in our grade <br />12 advanced functions course we are to graph rational functions that are reciprocals of linear and quadratic functions and ones where both the numerator and denominator are linear functions. In this post there are several activities (both hands on and electronic) that could be used throughout a unit on graphing Rational Funcitons. Here, we start with an investigation that is done with students in groups graphing reciprocal linear and quadratic functions by hand and then ends with a Desmos Card sort. There is also a Desmos investigation on functions in the form <a href="https://www.codecogs.com/eqnedit.php?latex=f(x)=&amp;space;\frac{ax+b}{cx+d}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?f(x)=&amp;space;\frac{ax+b}{cx+d}" title="f(x)= \frac{ax+b}{cx+d}" /></a>&nbsp; and a consolidation activity using Desmos Marbleslides. Lastly, there is an assignment challenging students to create their own <a href="http://wodb.ca/" target="_blank">Which One Doesn't Belong</a>. Note that you may not want to do all of these activities while doing this unit. Just pick and choose.<br /><a href="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAglEYBLiwXpC3aBc223OTxwCPcB/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAglEYBLiwXpC3aBc223OTxwCPcB/s320/EM_Curriculum.png" width="320" /></a><br /><ul><li>MHF4U 2.1 - determine, through investigation with and without technology, key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, positive/negative intervals, increasing/decreasing intervals) of the graphs of rational functions that are the reciprocals of linear and quadratic functions, and make connections between the algebraic and graphical representations of these rational functions.</li><li>MHF4U 2.2 - determine, through investigation with and without technology, key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, positive/negative intervals, increasing/decreasing intervals) of the graphs of rational functions that have linear expressions in the numerator and denominator, and make connections between the algebraic and graphical representations of these rational functions </li><li>MHF4U 2.3 - sketch the graph of a simple rational function using its key features, given the algebraic representation of the function</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://3.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFraklMQHtndVskF77GmYhgGDGwCPcB/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFraklMQHtndVskF77GmYhgGDGwCPcB/s320/EM_Materials.png" width="320" /></a></div><ul><li>Chart paper or <a href="http://slamdunkmath.blogspot.ca/2014/08/vertical-non-permanent-surfaces-and.html" target="_blank">vertical surfaces</a> for the investigation (markers etc)</li><li>If you choose to do the hands on card sort then you need to make copies of <a href="https://drive.google.com/open?id=0B9algQOOR_bkeC0ybUdTSnN3RFU" target="_blank">this set</a> of cards (one per group). We usually make these on card stock and laminate them for durability.</li><li>If you choose to do the Desmos card sort then you need to have technology for your students.&nbsp;</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cpagYRup3TCO3EN4S8OgGzACPcB/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cpagYRup3TCO3EN4S8OgGzACPcB/s320/EM_Procedure.png" width="320" /></a></div><h3 style="clear: both; text-align: left;">Activity 1: Reciprocal linear and quadratic functions</h3><div class="separator" style="clear: both; text-align: left;"></div><div class="separator" style="clear: both; text-align: center;"></div><ol><a href="https://1.bp.blogspot.com/-dbqSwZES198/WFhEO7ZGbZI/AAAAAAAABqI/RjYOih7QVT8bQBosvU8sRYDJUyp-Wpa5ACEw/s1600/RationalFunctionsAnswers.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://1.bp.blogspot.com/-dbqSwZES198/WFhEO7ZGbZI/AAAAAAAABqI/RjYOih7QVT8bQBosvU8sRYDJUyp-Wpa5ACEw/s200/RationalFunctionsAnswers.png" width="165" /></a><li>Put students in groups of no more than three. They can work on <a href="http://slamdunkmath.blogspot.ca/2014/08/vertical-non-permanent-surfaces-and.html" target="_blank">vertical surfaces</a> or at a table.</li><li>Each group is given <a href="https://drive.google.com/open?id=0B9algQOOR_bkbV9RWGdYbjVBTDQ" target="_blank">one set of a linear equation</a> and its corresponding reciprocal (or rational) function. There is enough sets for 11 groups. They are to graph each on the same axis. Afterwards they should determine any intercepts and/or equations of asymptotes (see answers to the right).</li><li>Once complete they should walk around the class to see other sets and come to some conclusions as to properties of linear functions and their corresponding rational functions.</li><li>Once complete there is a couple of follow up questions to check their thinking.&nbsp;</li><li>Next each group gets a set of quadratic functions and corresponding rational function. They are to graph each on the same axis. Afterwards they should determine any intercepts and/or equations of asymptotes.&nbsp;<div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-TyGGqOYa_EE/WLB9osMmGJI/AAAAAAAACXk/6BtYrWYVGkAgu4g7uD-RwgSS_v7el-PMwCEw/s1600/RationalCardsort.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="164" src="https://4.bp.blogspot.com/-TyGGqOYa_EE/WLB9osMmGJI/AAAAAAAACXk/6BtYrWYVGkAgu4g7uD-RwgSS_v7el-PMwCEw/s200/RationalCardsort.png" width="200" /></a></div></li><li>Again, once complete, they should walk around the class to see other sets and come to some conclusions.&nbsp;</li><li>There is another set of follow up questions to check their thinking (note, if time is a problem students can do a similar investigation for homework with <a href="https://teacher.desmos.com/activitybuilder/custom/585966d35eb50ea105005cdb" target="_blank">this Desmos</a> activity instead of the above steps).&nbsp;</li><li>As a follow up (maybe next day) you can do <a href="https://drive.google.com/open?id=0B9algQOOR_bkeC0ybUdTSnN3RFU" target="_blank">this physical card sort</a> or <a href="https://teacher.desmos.com/activitybuilder/custom/581166df0436f1e60592aa04" target="_blank">this Desmos card sort</a>. The Desmos card sort has some follow up questions to consolidate some of the ideas.&nbsp;</li></ol><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-XKFM7yUIM1Y/WK-w4WsICmI/AAAAAAAACV0/cuauQJ2XytQFMXxqXWE2UtUGT3KjGgvSwCLcB/s1600/Desmos%2BReciprocals.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><br /></a><a href="https://1.bp.blogspot.com/-XKFM7yUIM1Y/WK-w4WsICmI/AAAAAAAACV0/cuauQJ2XytQFMXxqXWE2UtUGT3KjGgvSwCLcB/s1600/Desmos%2BReciprocals.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-XKFM7yUIM1Y/WK-w4WsICmI/AAAAAAAACV0/cuauQJ2XytQFMXxqXWE2UtUGT3KjGgvSwCLcB/s400/Desmos%2BReciprocals.gif" width="560" /></a></div><h3>Activity 2 Graphs in the form&nbsp;<a href="https://www.codecogs.com/eqnedit.php?latex=f(x)=&amp;space;\frac{ax+b}{cx+d}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?f(x)=&amp;space;\frac{ax+b}{cx+d}" title="f(x)= \frac{ax+b}{cx+d}" /></a>&nbsp;</h3><a href="https://4.bp.blogspot.com/-sE01P391yWI/WLB3rFj2-hI/AAAAAAAACXI/k2jJt-c8sqExP45oIjfLCT69hPHhz0IGwCLcB/s1600/CopyGoogleForm.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://4.bp.blogspot.com/-sE01P391yWI/WLB3rFj2-hI/AAAAAAAACXI/k2jJt-c8sqExP45oIjfLCT69hPHhz0IGwCLcB/s200/CopyGoogleForm.png" width="185" /></a><br /><ol><li>Students complete the <a href="https://teacher.desmos.com/activitybuilder/custom/5812204c56f79a01065dc84d" target="_blank">Desmos Investigation</a>. This can be done in class or as a homework assignment.</li><li>As consolidation, students can check what they know with <a href="https://drive.google.com/open?id=0B9algQOOR_bkUHgwLVdwT1FPMmM" target="_blank"><span id="goog_582246367"></span>this quiz<span id="goog_582246368"></span></a>. This can be done using paper and pencil (copy double sided then cut in half) or via this online <a href="https://docs.google.com/a/mytools2go.ca/forms/d/e/1FAIpQLSfBiaPv-KvZNzFLunPkY-zgVSjogqQKe4snRWs0V1K9hoNqCQ/viewform" target="_blank">Google Form</a>. Note that if you use the form, click on <a href="https://drive.google.com/open?id=1olgvSXTUrlcSrTbwqLFAL2hwlljuDQPirfihyeBKEFU" target="_blank">this link</a> and then choose advanced options (3 vertical dots) to make a copy. Please do not edit our form.</li></ol><h3>Activity 3: Desmos MarbleSlides for&nbsp;<a href="https://www.codecogs.com/eqnedit.php?latex=f(x)=&amp;space;\frac{ax+b}{cx+d}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?f(x)=&amp;space;\frac{ax+b}{cx+d}" title="f(x)= \frac{ax+b}{cx+d}" /></a>&nbsp;</h3><div><ol><li>To show if they understand the investigation from Activity 2, students can complete this Desmos <a href="https://teacher.desmos.com/activitybuilder/custom/5814e9af571d8ae610926d27" target="_blank">MarbleSlides</a>. The first few slides are just to show some possible solutions and then the challenges start. Note that students may have to work with the domain of the function to become successful.&nbsp;</li></ol><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-u3jLKgQj9q8/WLB7CjW1snI/AAAAAAAACXU/dKZflKn5nzsgD0vmb9hbrhyIU7cwLOXAgCLcB/s1600/RationalMarbleslides.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-u3jLKgQj9q8/WLB7CjW1snI/AAAAAAAACXU/dKZflKn5nzsgD0vmb9hbrhyIU7cwLOXAgCLcB/s400/RationalMarbleslides.gif" width="560" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">If you want to know how to create your own Marbleslides, watch this video</div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/c9R6_Pt-ktY/0.jpg" frameborder="0" height="315" src="https://www.youtube.com/embed/c9R6_Pt-ktY?feature=player_embedded" width="530"></iframe></div></div><h3>Activity 4: Which One Doesn't Belong Assignment</h3><ol><li>As a review you might choose to assign students to create <a href="https://drive.google.com/open?id=0B9algQOOR_bkQWhIZTV1dHJic2s" target="_blank">their own</a> Which One Doesn't Belong (<a href="http://wodb.ca/" target="_blank">http://wodb.ca/</a>). The goal here is to create four graphs such that each of the graphs could be chosen as the one that doesn't belong based on specific criteria.</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="https://3.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6E-q1VkeGwQKEH9LGbINliCgCPcB/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6E-q1VkeGwQKEH9LGbINliCgCPcB/s320/EM_Downloads.png" width="320" /></a></div><ul><li>Activity 1 Investigation (<a href="https://drive.google.com/open?id=0B9algQOOR_bkbV9RWGdYbjVBTDQ" target="_blank">PDF</a>, <a href="https://drive.google.com/open?id=1JGU5Btx3mwIpXKMKGVIBxa8HmDMZDNSfaVtT5oy1MV4" target="_blank">Google Doc</a>, <a href="https://teacher.desmos.com/activitybuilder/custom/585966d35eb50ea105005cdb" target="_blank">Desmos</a>)</li><li>Activity 1 Card Sort (<a href="https://drive.google.com/open?id=0B9algQOOR_bkeC0ybUdTSnN3RFU" target="_blank">PDF</a>, <a href="https://drive.google.com/open?id=1uEV52Ra-Meo_HBvF_qx-1MKrEWybdq5P6OqFtiKLLYE" target="_blank">Google Doc</a>, <a href="https://teacher.desmos.com/activitybuilder/custom/581166df0436f1e60592aa04" target="_blank">Desmos</a>)</li><li>Activity 2 Investigation (<a href="https://teacher.desmos.com/activitybuilder/custom/5812204c56f79a01065dc84d" target="_blank">Desmos</a>)</li><li>Activity 2 Homework Quiz (<a href="https://drive.google.com/open?id=0B9algQOOR_bkUHgwLVdwT1FPMmM" target="_blank">PDF</a>, <a href="https://drive.google.com/open?id=1D02hrv0qc-HKtI-eR0Xpn_KoqDWkyM3VBeLMhk0t9F0" target="_blank">Google Doc</a>, <a href="https://drive.google.com/open?id=1olgvSXTUrlcSrTbwqLFAL2hwlljuDQPirfihyeBKEFU" target="_blank">Online form</a> - make a copy, don't edit ours)</li><li>Activity 3 Marble Slides (<a href="https://teacher.desmos.com/activitybuilder/custom/5814e9af571d8ae610926d27" target="_blank">Desmos</a>)</li><li>Activity 4 Which One Doesn't Belong (<a href="https://drive.google.com/open?id=0B9algQOOR_bkQWhIZTV1dHJic2s" target="_blank">PDF</a>, <a href="https://drive.google.com/open?id=1p0dyTJQQIrzmLqHwymvW1ucY7xfmh-XdXuZdWiIc56U" target="_blank">Google Doc</a>)</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks&nbsp;</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-55019231263102578052017-01-16T14:20:00.001-05:002017-01-16T14:21:13.339-05:00Equation Strips<div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EOtR_fu1wjGcRR5kJ3oShmwCPcB/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EOtR_fu1wjGcRR5kJ3oShmwCPcB/s320/EM_Activity.png" width="320" /></a></div><a href="https://1.bp.blogspot.com/-cykzQN7JDuc/WH0cePKFTbI/AAAAAAAABw0/vgsg6XNIHMAUxtfXobbydFls7rfDxHDBwCLcB/s1600/EquationStrips.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-cykzQN7JDuc/WH0cePKFTbI/AAAAAAAABw0/vgsg6XNIHMAUxtfXobbydFls7rfDxHDBwCLcB/s320/EquationStrips.jpg" width="320" /></a>In Ontario our grade 7 students are introduced to solving simple equations in the form ax&nbsp;+ b = c where the values of a, b and c are whole numbers. We think it's a good idea for them to start by having some sort of visual representation of each equation. In this activity, students are given 16 cards that correspond to 16 equations represented as strips (the top and bottom of the strips represent the left and right sides of the equations). Students solve for x given the strips and then rewrite the algebraic form equation. <br /><div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAglEYBLiwXpC3aBc223OTxwCPcB/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAglEYBLiwXpC3aBc223OTxwCPcB/s320/EM_Curriculum.png" width="320" /></a></div><ul><a href="https://3.bp.blogspot.com/-J5IfxI4wEXQ/WH0LjI_BYwI/AAAAAAAABuI/ROxMxZ5TUFYMuNb-qEhgkTYQTfbDl9R4QCLcB/s1600/EquationStripsCards.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://3.bp.blogspot.com/-J5IfxI4wEXQ/WH0LjI_BYwI/AAAAAAAABuI/ROxMxZ5TUFYMuNb-qEhgkTYQTfbDl9R4QCLcB/s200/EquationStripsCards.png" width="159" /></a><li><b>Grade 7 Patterning &amp; Algebra</b> - solve linear equations of the form ax <span class="s1">= </span>c or c <span class="s1">= </span>ax and ax + b <span class="s1">= </span>c or variations such as b + ax <span class="s1">= </span>c and c <span class="s1">= </span>bx + a (where a, b, and c are natural numbers) by modelling with concrete materials, by inspection, or by guess and check, with and without the aid of a calculator&nbsp;</li><li><b>Grade 8 Patterning &amp; Algebra </b>- as review</li></ul><a href="https://3.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFraklMQHtndVskF77GmYhgGDGwCPcB/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFraklMQHtndVskF77GmYhgGDGwCPcB/s320/EM_Materials.png" width="320" /></a><br /><ul><li>Each group gets a set of <a href="https://drive.google.com/open?id=0B9algQOOR_bkQ2s0T0tRdUlnWE0" target="_blank">16 cards</a></li><li>Make several copies of the cards on card stock and laminate them so they last longer. You may wish to copy each set onto a different colour so that if they get mixed up you know each set by their colour.</li><li>Cut out the cards so that each group gets a set of 16.&nbsp;</li></ul><a href="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cpagYRup3TCO3EN4S8OgGzACPcB/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cpagYRup3TCO3EN4S8OgGzACPcB/s320/EM_Procedure.png" width="320" /></a><br /><ol><a href="https://4.bp.blogspot.com/-Aih2vGO3wR0/WHjf6NQv8zI/AAAAAAAABsY/Ci9Jsowtfb0szD4fSpY1iwe6yjq-V-1jwCPcB/s1600/EquationStrips.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="148" src="https://4.bp.blogspot.com/-Aih2vGO3wR0/WHjf6NQv8zI/AAAAAAAABsY/Ci9Jsowtfb0szD4fSpY1iwe6yjq-V-1jwCPcB/s200/EquationStrips.png" width="200" /></a><li>Each group of 2-3 students gets one full set of 16 cards.&nbsp;</li><li>Students are to determine the value of x for each card.</li><li>Once determining x then they should then determine the algebraic expression for each card</li><li>You can circulate with the <a href="https://drive.google.com/open?id=0B9algQOOR_bkSjBrcmpyRFhsUlk" target="_blank">solution card</a> to check answers.</li><li>Once finished you can create your own cards using <a href="http://mail.wecdsb.on.ca/~david_petro/WebSketches/EquationStrips/index.html" target="_blank">this web sketch</a>. This allows you to change the coefficients of a, b &amp; c and it generates all four possible configurations. This web sketch assumes that a, b &amp; c will be whole numbers and will not allow any solutions that have x as negative. Once you put your coefficients in then take a screenshot,&nbsp;<span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px;">use the screen capture software of your choice to copy and paste the version you want to use (For Windows use the&nbsp;</span><a href="https://support.microsoft.com/en-ca/help/13776/windows-use-snipping-tool-to-capture-screenshots" style="background-color: white; color: #7ba2d3; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; text-decoration: none;" target="_blank">Snipping Tool</a><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px;">,&nbsp;for Chromebooks use&nbsp;</span><a href="https://support.google.com/chromebook/answer/183101?source=gsearch&amp;hl=en" style="background-color: white; color: #7ba2d3; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; text-decoration: none;" target="_blank">Shift CTRL F5</a><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px;">,&nbsp;for Macs use&nbsp;</span><a href="http://www.imore.com/screenshot-mac" style="background-color: white; color: #7ba2d3; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; text-decoration: none;" target="_blank">Command Shift 4</a><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px;">, or iPad use the&nbsp;</span><a href="https://support.apple.com/en-ca/HT200289" style="background-color: white; color: #7ba2d3; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; text-decoration: none;" target="_blank">Home and Sleep</a><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px;">&nbsp;buttons together. You can then paste into the word processor of your choice.&nbsp;</span></li></ol><div class="separator" style="clear: both; text-align: left;"><a href="https://3.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6E-q1VkeGwQKEH9LGbINliCgCPcB/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6E-q1VkeGwQKEH9LGbINliCgCPcB/s320/EM_Downloads.png" width="320" /></a></div><ul><li>Equation Strip Cards Print version (<a href="https://drive.google.com/open?id=1DgVC9XGEuopSftiVoQUkGmbBWTefXKFxCX_jMq5GN98" target="_blank">Google Doc</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkQ2s0T0tRdUlnWE0" target="_blank">PDF</a>)</li><li>Equation Strip Solution card (<a href="https://drive.google.com/open?id=1ZpsKFVK0ZrL3KAJ9pnPIBOW9sf2OHsVkVIIn-uI9jYE" target="_blank">Google Doc</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkSjBrcmpyRFhsUlk" target="_blank">PDF</a>)</li><li>Equation Strip Solution <a href="https://drive.google.com/drive/folders/0B9algQOOR_bkWURKQUxjM2RzaEU" target="_blank">template</a></li><li>Equation Strip <a href="http://mail.wecdsb.on.ca/~david_petro/WebSketches/EquationStrips/index.html" target="_blank">Web Sketch</a></li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks&nbsp;</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-43467201754516401682016-12-04T22:22:00.001-05:002016-12-04T22:23:58.376-05:00Introducing Histograms<br /><div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EOtR_fu1wjGcRR5kJ3oShmwCPcB/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/2tzf72Qes-EOtR_fu1wjGcRR5kJ3oShmwCPcB/s320/EM_Activity.png" width="320" /></a></div><a href="https://1.bp.blogspot.com/-rFKUioqqZXc/WESeBwvC28I/AAAAAAAABmY/nlO4S_mFqf0RSZtHis4GzL22W8D3JGSxACLcB/s1600/HistogramSort.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-rFKUioqqZXc/WESeBwvC28I/AAAAAAAABmY/nlO4S_mFqf0RSZtHis4GzL22W8D3JGSxACLcB/s320/HistogramSort.JPG" width="320" /></a>In grade 8 in Ontario histograms are one of the new data management topics. Below is a series of activities that range from paper &amp; pencil to virtual manipulatives. They start by a simple comparison of bar graphs and histograms to identify characteristics, then moves to some consolidation of ideas using a Desmos Sort. Then some data collection of student heights to formally introduce creating a histogram followed by some practice making histograms by hand and then with Google Sheets. If you did everything here it should take about 2-3 classes.<br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAglEYBLiwXpC3aBc223OTxwCPcB/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/ur8pPm7VpnAglEYBLiwXpC3aBc223OTxwCPcB/s320/EM_Curriculum.png" width="320" /></a></div>Grade 8<br /><ul><a href="https://4.bp.blogspot.com/-FEHyoKWGO0c/WETXrKJZYJI/AAAAAAAABnI/Yye20Vz66UE20_dceYzSWtsE4cLMoJIcwCLcB/s1600/HistogramCardsort.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="147" src="https://4.bp.blogspot.com/-FEHyoKWGO0c/WETXrKJZYJI/AAAAAAAABnI/Yye20Vz66UE20_dceYzSWtsE4cLMoJIcwCLcB/s320/HistogramCardsort.png" width="320" /></a><li>collect and organize categorical, discrete, or continuous primary data and secondary data (e.g., electronic data from websites such as E-Stat or Census At Schools), and display the data in charts, tables, and graphs (including histograms and scatter plots) that have appropriate titles, labels (e.g., appropriate units marked on the axes), and scales (e.g., with appropriate increments) that suit the range and distribution of the data, using a variety of tools (e.g., graph paper, spreadsheets, dynamic statistical software);&nbsp;</li><li>select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph (i.e., from types of graphs already studied, including histograms and scatter plots);<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-QhWgZ_p1Ks8/WETX4rN-a9I/AAAAAAAABnM/94vxfgCzg_glfBkQqLZkfaTB41DissOKgCEw/s1600/HistogramConsolidation.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="148" src="https://2.bp.blogspot.com/-QhWgZ_p1Ks8/WETX4rN-a9I/AAAAAAAABnM/94vxfgCzg_glfBkQqLZkfaTB41DissOKgCEw/s320/HistogramConsolidation.png" width="320" /></a></div></li><li>read, interpret, and draw conclusions from primary data (e.g., survey results, measurements, observations) and from secondary data (e.g., election data or temperature data from the newspaper, data from the Internet about lifestyles), presented in charts, tables, and graphs (including frequency tables with intervals, histograms, and scatter plots);</li><li>demonstrate an understanding of the appropriate uses of bar graphs and histograms by comparing their characteristics</li><li>Could also be used as a review in MBF3C or MDM4U</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://3.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFraklMQHtndVskF77GmYhgGDGwCPcB/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/pDw8f3oFraklMQHtndVskF77GmYhgGDGwCPcB/s320/EM_Materials.png" width="320" /></a></div><ul><a href="https://1.bp.blogspot.com/-rxH4q9iKUPw/WEStTF00A9I/AAAAAAAABmw/Jt38Q4Yj5dUOnUW-oXPDP69bWDKyV-NpgCLcB/s1600/HistogramSort.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://1.bp.blogspot.com/-rxH4q9iKUPw/WEStTF00A9I/AAAAAAAABmw/Jt38Q4Yj5dUOnUW-oXPDP69bWDKyV-NpgCLcB/s200/HistogramSort.png" width="155" /></a><li>If you are doing the physical card sort then <a href="https://drive.google.com/open?id=0B9algQOOR_bkMUlTWjFOdmwyblk" target="_blank">print graphs</a> to card stock (we suggest each set is a different colour so that if students mix them up they are easy to separate). We also suggest lamination. There are two pages for a total of 16 cards.&nbsp;</li><li>If you are doing any of the online activities then chromebooks/laptops/computers/iPads will be needed. You will also need to make copies of the Desmos version of the <a href="https://teacher.desmos.com/activitybuilder/custom/5836033b93f58ce0069506e7" target="_blank">card sort</a> and/or the Desmos card sort consolidation.</li><li>Copies of the <a href="https://drive.google.com/open?id=0B9algQOOR_bkb3dPSkFhWkJ1Zms" target="_blank">handout</a>.&nbsp;</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cpagYRup3TCO3EN4S8OgGzACPcB/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/_DH5faCac8cpagYRup3TCO3EN4S8OgGzACPcB/s320/EM_Procedure.png" width="320" /></a></div><ol><li>The purpose of the card sort is to start to distinguish both histograms and bar graphs and continuous vs categorical data. But first have them do an open sort. Hand out cards to students (or give students the code for the <a href="https://teacher.desmos.com/activitybuilder/custom/5836033b93f58ce0069506e7" target="_blank">Desmos Sort</a>). Ask them to sort them in any way they wish. The only stipulations are that there should be at least two groups and each group must have at least two cards. Students will sort them in all kids of ways (by the numbers, by the topics, by the looks). Circulate and encourage them to explain how they were sorted.</li><li>Once sorted it is likely that most will not have them sorted how you wish. Have them describe their sorts then ask them to sort them in a way so that there are only two groups.&nbsp;</li><li>By this time some may have them sorted into bar graphs and histograms. If not show one bar graph and then one histogram stating that you want those cards to represent characteristics of each group (you can use the <a href="https://drive.google.com/open?id=157gmjYf7SlucqLIkxgc4TQrPRdBrW1pA05rkY-kp4p8" target="_blank">slideshow</a> to show the graphs). Use these graphs to develop the difference between continuous and discrete data.<div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/--hr1OYQyCP4/WETcpzuFt9I/AAAAAAAABnc/A04EWeqOH8klP3VxwtE8biVAPKtCbqOFgCLcB/s1600/HistogramWorksheet.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/--hr1OYQyCP4/WETcpzuFt9I/AAAAAAAABnc/A04EWeqOH8klP3VxwtE8biVAPKtCbqOFgCLcB/s320/HistogramWorksheet.png" width="248" /></a></div></li><li>Time to change the pace and have students collect some data. Have students measure their heights and put them on a dot plot on the board. Use this to create a histogram (without creating a tally). You might want to collect their heights in a spreadsheet so that you can create a histogram with it later.&nbsp;</li><li>Walk through the front of the <a href="https://drive.google.com/open?id=0B9algQOOR_bkb3dPSkFhWkJ1Zms" target="_blank">handout</a> to show how to create a histogram from data.&nbsp;</li><li>Likely you will be at least done one class at this point (if not more). At the beginning of the second class, start with the <a href="https://teacher.desmos.com/activitybuilder/custom/5835e9ec042e4890162ea0c9" target="_blank">consolidation Desmos</a> card sort (with some stuff on average) to remind students of continuous and discrete data. Another possible way to start is to have students use this <a href="https://drive.google.com/open?id=1h4o-cuxHtNEHkhTUo59Q0OGvi6ZzijJj_TOA9Pmg30o" target="_blank">Google form</a> to enter some examples of continuous and discrete data. You can take up the results.&nbsp;</li><li>Once done taking up the worksheet you can then introduce students to creating histograms using Google Sheets. Share <a href="https://drive.google.com/open?id=1wBNR5v9uWC9eaX4YKpYAlXtW8GQtb3ZQDSH5Spqdpt0" target="_blank">this sheet</a> with continuous data. This <a href="https://www.youtube.com/watch?v=9LCJ33MnOlA&amp;index=5&amp;list=PLre81yNdo4MxHwH7i4gfZpnRJERmrRrW0&amp;t=7s" target="_blank">video</a> will tell you how.&nbsp;</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="https://3.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6E-q1VkeGwQKEH9LGbINliCgCPcB/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/q3pQzDA6G6E-q1VkeGwQKEH9LGbINliCgCPcB/s320/EM_Downloads.png" width="320" /></a></div><ul><li>Card Sort <a href="https://drive.google.com/open?id=1IuhUtfr1xmfIQ8__V0NT84iIT1-RdoiG6Qoz11djrAY" target="_blank">Google Docs</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkMUlTWjFOdmwyblk" target="_blank">PDF</a>, <a href="https://teacher.desmos.com/activitybuilder/custom/5836033b93f58ce0069506e7" target="_blank">Desmos</a>&nbsp;<a href="https://drive.google.com/open?id=157gmjYf7SlucqLIkxgc4TQrPRdBrW1pA05rkY-kp4p8" target="_blank">Slide show of each graph</a></li><li>Desmos <a href="https://teacher.desmos.com/activitybuilder/custom/5835e9ec042e4890162ea0c9" target="_blank">Consolidation</a></li><li>Handout <a href="https://drive.google.com/open?id=1t3_ef_iR50aWtEys6CfGoXUMFPISJSv7UH8Mwc4zrtM" target="_blank">Google Docs</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkb3dPSkFhWkJ1Zms" target="_blank">PDF</a>&nbsp;</li><li>Handout Answers <a href="https://drive.google.com/open?id=1UK277Kyy7PeGMuDXT-NHf4F6sDe-ZZL7G3gMV70ToOA" target="_blank">Google Docs</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkb3dPSkFhWkJ1Zms" target="_blank">PDF</a></li><li>Discrete/Continuous <a href="https://drive.google.com/open?id=1h4o-cuxHtNEHkhTUo59Q0OGvi6ZzijJj_TOA9Pmg30o" target="_blank">Form</a></li><li>Spreadsheet <a href="https://drive.google.com/open?id=1wBNR5v9uWC9eaX4YKpYAlXtW8GQtb3ZQDSH5Spqdpt0" target="_blank">Graphs</a>, <a href="https://drive.google.com/open?id=1Z6Z1Ikb4CGgJbIJ1HBbX2t8B7En_O1F1yUePFeh4qO4" target="_blank">Answers</a></li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks&nbsp;</span><br /><br /><style type="text/css">p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times} </style><style type="text/css">p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times} </style><style type="text/css">p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times} </style>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-70333606725931482032016-06-20T14:05:00.000-04:002016-06-26T11:43:53.831-04:00Developing Derivatives Graphically<div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/R5BYfFdfhTsb1HaN1X6G36VltuH8wIIMwCKgB/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/R5BYfFdfhTsb1HaN1X6G36VltuH8wIIMwCKgB/s320/EM_Activity.png" width="320" /></a></div><a href="https://4.bp.blogspot.com/-NBdKPbRRRjk/V2Q-nNV8ZUI/AAAAAAAABT8/k5NY9F-HoyAqyW9ICp9msv9WxoRTnfi7wCLcB/s1600/Derivatives2.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-NBdKPbRRRjk/V2Q-nNV8ZUI/AAAAAAAABT8/k5NY9F-HoyAqyW9ICp9msv9WxoRTnfi7wCLcB/s320/Derivatives2.JPG" width="320" /></a>In this activity students develop the visual connection between a quadratic function and its derivative. Each student is given a quadratic function and an x value. They are to determine the point and the instantaneous rate of change of their function at that x value. Once they do this they plot their point and then also plot their rate of change (as a point at that x value) on a piece of chart paper. Since everyone is given a different x value, a graph of both the original function and its derivative should be constructed. This would be a good activity to introduce the concept of the derivative shortly after students know how to find the instantaneous rate of change by using a limit.<br />Once students are done the graphs on the charts, they can then move to extend their thinking with <a href="https://teacher.desmos.com/activitybuilder/custom/571ed42ef68cf5f10ee49d22#" target="_blank">this Desmos</a> activity where they visually estimate the slope of the tangent to eventually build the derivative (based on a <a href="https://www.desmos.com/calculator/a9qu2gphzj" target="_blank">original sketch</a> by <a href="https://twitter.com/eluberoff" target="_blank">@eluberoff</a>). As they slide the sliders to estimate each tangent, once they get them all close to where they should be, the derivative appears (see animated gif below)They do this for several simple quadratic functions and (hopefully) see the beginnings of how the power rule works as they move towards simple cubic functions.<br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/LBEopg7S9sY/0.jpg" frameborder="0" height="315" src="https://www.youtube.com/embed/LBEopg7S9sY?feature=player_embedded" width="530"></iframe></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/uaC8TnO-r6IfwzPfxYnZG_GHApgI62BoQCKgB/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/uaC8TnO-r6IfwzPfxYnZG_GHApgI62BoQCKgB/s320/EM_Curriculum.png" width="320" /></a></div><ul><a href="https://3.bp.blogspot.com/-IO5Y8-abaXc/V2Q-wDQJpjI/AAAAAAAABUE/DMUuanYx0Fc7AWDneTXoefj8tiPQn9QtwCLcB/s1600/Derivative.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="205" src="https://3.bp.blogspot.com/-IO5Y8-abaXc/V2Q-wDQJpjI/AAAAAAAABUE/DMUuanYx0Fc7AWDneTXoefj8tiPQn9QtwCLcB/s320/Derivative.gif" width="320" /></a><li>MCV4U-A2.2 - generate, through investigation using technology, a table of values showing the instantaneous rate of change of a polynomial function, f(x), for various values of x (e.g., construct a tangent to the function, measure its slope, and create a slider or animation to move the point of tangency), graph the ordered pairs, recognize that the graph represents a function called the derivative, f ’(x) or dy/dx , and make connections between the graphs of f(x) and f ’(x) or y and dy/dx</li><li>A3.1 - verify the power rule for functions of the form f(x) <span class="s1">= </span>x<sup>n</sup> , where n is a natural number</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/9TU7hJ1FqxgjkfAJNUaMXPsRkVwiaEJiwCKgB/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/9TU7hJ1FqxgjkfAJNUaMXPsRkVwiaEJiwCKgB/s320/EM_Materials.png" width="320" /></a></div><ul><a href="https://1.bp.blogspot.com/-TWx32jBKUpg/V2Q_fLLx8LI/AAAAAAAABUQ/h2Ts3pFxKEIam_SxftlO9DzAAPo-K7hZQCLcB/s1600/Derivatives4.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="191" src="https://1.bp.blogspot.com/-TWx32jBKUpg/V2Q_fLLx8LI/AAAAAAAABUQ/h2Ts3pFxKEIam_SxftlO9DzAAPo-K7hZQCLcB/s200/Derivatives4.png" width="200" /></a><li>Grid chart paper (one per function - write a different function on the top of each piece). You may wish to draw the grid on each piece before hand. Because the scale can get disproportionally large on the y vs x axis you may want to spread the scale out on the x so that it's not so crowded. <b><u>Note</u></b> that if you choose to us a disproportionate scale on the chart paper then the kids must use a similar scale in their mini graph papers ( I've done this activity a few times and only now, as I created this post, did I figure out that this is why the slopes of the tangents didn't quite match the graphs physically).&nbsp;</li><li>Copies of each mini graph for each student via the handout (see image to the right for a sample). There are four functions (f(x) = 1/4x<sup>2</sup>, f(x) = 1/2x<sup>2</sup>, f(x) = x<sup>2</sup>, and f(x) = 2x<sup>2</sup>) and potentially nine x values for each function (-4, -3, ....3, 4). You may not want to give out the -4 or 4 for the&nbsp;f(x) = 2x<sup>2</sup>&nbsp;function as it&nbsp;requires a big y axis scale. Depending on how big your class is, you may not want to hand out all of the mini graph sheets. For example, if you had 25 students you might want to use 3 of the functions. Cut these out ahead of time. You may wish to have more than you need ready so that if someone finished quickly, they can be given another one.&nbsp;</li><li>Scotch tape for students to stick their graphs on the chart paper.</li><li>Markers. Preferably different colours (one colour for the function points, derivative points, function line, derivative line and tangent lines).</li><li>Laptops, Chromebooks, iPads if you will be extending this to the Desmos version</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/3Tqwo7SQmiENkZhfqRT0IlrQnTEPhY3lACKgB/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/3Tqwo7SQmiENkZhfqRT0IlrQnTEPhY3lACKgB/s320/EM_Procedure.png" width="320" /></a></div><ul><a href="https://3.bp.blogspot.com/-FoTnEm6aJHo/V2RDBQDSSrI/AAAAAAAABU0/SZRGtuAPtbYeiaIc8REEMdb4hw5ap7dngCLcB/s1600/Derivatives6.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-FoTnEm6aJHo/V2RDBQDSSrI/AAAAAAAABU0/SZRGtuAPtbYeiaIc8REEMdb4hw5ap7dngCLcB/s320/Derivatives6.jpg" width="320" /></a><li>Place chart paper on the walls and distribute one mini graph to each student. Make sure there is enough of each function so that the shape will be visible</li><li>Each student then does the following:</li></ul><ol style="margin-bottom: 0pt; margin-top: 0pt;"><li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: &quot;arial&quot;; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Determine the point on that function at that x value: A( &nbsp;&nbsp;&nbsp;&nbsp;, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;)</span></div></li><li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: &quot;arial&quot;; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Determine the slope of the tangent at that x value for your function: Slope of tangent = _____</span></div></li><li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: &quot;arial&quot;; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">On your mini graph, draw a line with the same slope as the slope you just calculated and going through the middle point on the mini graph</span></div></li><li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: &quot;arial&quot;; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Plot the point from #1 on the large graph. Stick your mini graph on the large graph paper so the point on the mini graph paper is on top of the point you just plotted (be careful with your orientation)</span></div></li><li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: black; font-family: &quot;arial&quot;; font-size: 14.666666666666666px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Plot a second point that has your x value and its y value is the slope of your tangent: B( &nbsp;&nbsp;, &nbsp;&nbsp;)</span></li></ol><div><ul><li><span style="font-family: &quot;arial&quot;; font-size: 14.6667px; white-space: pre-wrap;">As students plot their points by sticking their mini graphs on the chart paper, you may wish to use the markers to draw over their points and lines to make them more visible. Note: If a student makes a mistake, do not correct it right away (or make it permanent with a marker). Instead ask students if they think anything is out of place either at the time or during the consolidation</span></li><li><span style="font-family: &quot;arial&quot;; font-size: 14.6667px; white-space: pre-wrap;">Once all the graphs are done consolidate the ideas </span></li><li><span style="font-family: &quot;arial&quot;; font-size: 14.6667px; white-space: pre-wrap;">Once consolidated then move to the Desmos activity. If you have not done a Desmos activity before you might like to watch some of these tutorials first: <a href="https://www.youtube.com/watch?v=V3qS5PjX0xw" target="_blank">Navigating</a>, starting an <a href="https://www.youtube.com/watch?v=ZNbnbEYxMDk" target="_blank">activity</a>, and teacher <a href="https://www.youtube.com/watch?v=8c7Xpv99nvE" target="_blank">dashboard</a>.</span></li><li><span style="font-family: &quot;arial&quot;; font-size: 14.6667px; white-space: pre-wrap;">Note that it is not necessary for students to get all the way through the activity. As long as they get through the quadratics. The cubical are the extension. The whole idea behind this is they discover the power rule. </span></li></ul></div><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/5dYPDyufV98Usf1E9E5eDGoYWxd6ZsNAQCKgB/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/5dYPDyufV98Usf1E9E5eDGoYWxd6ZsNAQCKgB/s320/EM_Downloads.png" width="320" /></a></div><ul><li>Slope of the Tangent-mini graphs (Google <a href="https://drive.google.com/open?id=1MRpf1Eq6UZ31_GcvTcpf17sbkJwG2h-ImZvU0K6GH_Y" target="_blank">doc</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkdEtmWkJveWt5UXc" target="_blank">PDF</a>)</li><li>Desmos <a href="https://teacher.desmos.com/activitybuilder/custom/571ed42ef68cf5f10ee49d22#" target="_blank">activity</a></li><li>Suggestions from <a href="https://twitter.com/msphillips1618/status/746773571020668928" target="_blank">@MsPhillips1618</a> and <a href="https://twitter.com/Desmos/status/747080679993839616" target="_blank">@Desmos</a> too</li></ul><div><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span></div>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-89100902657904097472016-06-06T10:47:00.000-04:002016-12-01T07:41:30.400-05:00Derivative Matching Cards<div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/R5BYfFdfhTsb1HaN1X6G36VltuH8wIIMwCKgB/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/R5BYfFdfhTsb1HaN1X6G36VltuH8wIIMwCKgB/s320/EM_Activity.png" width="320" /></a></div><a href="https://4.bp.blogspot.com/-h0u4Oi403iE/V1WD59sSF_I/AAAAAAAABR0/mlZcP_4A6Ukc-0-ARuePPgbxqRPnyTNoACLcB/s1600/DerivativeMatch2.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-h0u4Oi403iE/V1WD59sSF_I/AAAAAAAABR0/mlZcP_4A6Ukc-0-ARuePPgbxqRPnyTNoACLcB/s320/DerivativeMatch2.JPG" width="320" /></a>This is a very simple matching activity for Calculus. Students are give a set of cards with either a linear, quadratic or cubic function on them. Their job is to pair them up so that one is a function and the other is its derivative. There are a total of 12 functions with 12 derivatives. The first six are all linear or quadratic graphs and the second six are either quadratic or cubic graphs (if you wanted to give students an easier set you could only give them the first six). This is not meant to be a brain buster of an activity but it does help to solidify thinking in terms of the characteristics of the connections between a function and its derivative.<br /><b><span style="color: red;">NEW:</span></b> Desmos has turned this activity into one of their new CardSort activities. You can get that version <a href="https://teacher.desmos.com/activitybuilder/custom/57b342ce867e43be309e0451" target="_blank">here</a><br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/uaC8TnO-r6IfwzPfxYnZG_GHApgI62BoQCKgB/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/uaC8TnO-r6IfwzPfxYnZG_GHApgI62BoQCKgB/s320/EM_Curriculum.png" width="320" /></a></div><div class="p1"></div><ul><a href="https://3.bp.blogspot.com/-XYkMj6dCAos/V7tbL-C1iOI/AAAAAAAABXs/6nw06xrw-ZMoWlHLpbnbqiMcXKQ58nyZwCLcB/s1600/Desmos-Calculus.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="232" src="https://3.bp.blogspot.com/-XYkMj6dCAos/V7tbL-C1iOI/AAAAAAAABXs/6nw06xrw-ZMoWlHLpbnbqiMcXKQ58nyZwCLcB/s320/Desmos-Calculus.png" width="320" /></a><li>MCV4U - A2.2 - generate, through investigation using technology, a table of values showing the instantaneous rate of change of a polynomial function, f(x), for various values of x (e.g., construct a tangent to the function, measure its slope, and create a slider or animation to move the point of tangency), graph the ordered pairs, recognize that the graph represents a function called the derivative, f ’(x) or , and make connections between the graphs of f(x) and f ’(x) or y and dy/dx</li><li>MCV4U - B1.1 - sketch the graph of a derivative function, given the graph of a function that is continuous over an interval, and recognize points of inflection of the given function (i.e., points at which the concavity changes)</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/9TU7hJ1FqxgjkfAJNUaMXPsRkVwiaEJiwCKgB/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/9TU7hJ1FqxgjkfAJNUaMXPsRkVwiaEJiwCKgB/s320/EM_Materials.png" width="320" /></a></div><ul><a href="https://3.bp.blogspot.com/-I-jZU5uYDY4/V1WHJWf5lPI/AAAAAAAABSA/7mcLxRhfscsNbFAj3O-XdmKqiHdq3CmpwCLcB/s1600/DerivativeMatch1.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-I-jZU5uYDY4/V1WHJWf5lPI/AAAAAAAABSA/7mcLxRhfscsNbFAj3O-XdmKqiHdq3CmpwCLcB/s320/DerivativeMatch1.png" width="249" /></a><li>As mentioned above, there are 12 cards and their derivatives but you could break them up into sets of 6 cards and their derivatives where the first set was made of linear and quadratic functions and the second set is made of quadratic and cubic functions (or you could just put them all together). On each page there are six graphs. The first column are the functions and the second column are the matching derivatives.</li><li>Print the sheets out on card stock (and laminate if possible). We tend to print each set out on different colours. This way if they get mixed up all you need to do is collect 24 cards of one colour and you will know you have a full set</li><li>You may also want to print a copy of the teacher answer key which has all 24 graphs on one page so you can easily check student's answers.</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/3Tqwo7SQmiENkZhfqRT0IlrQnTEPhY3lACKgB/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/3Tqwo7SQmiENkZhfqRT0IlrQnTEPhY3lACKgB/s320/EM_Procedure.png" width="320" /></a></div><ul><a href="https://1.bp.blogspot.com/-GvTFiT8Tz8s/V1WH5LGSPiI/AAAAAAAABSM/_iwOiB7kEDcnsr2Tyaoqfk_NjKyzmMRpQCLcB/s1600/DerivativeMatch3.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="199" src="https://1.bp.blogspot.com/-GvTFiT8Tz8s/V1WH5LGSPiI/AAAAAAAABSM/_iwOiB7kEDcnsr2Tyaoqfk_NjKyzmMRpQCLcB/s320/DerivativeMatch3.JPG" width="320" /></a><li>Put students in groups of two or three</li><li>Distribute cards and tell them they have to pair the cards up in terms of a function its derivative.&nbsp;</li><li>Instruct them that every card is paired up and they will likely be correct if they have no cards left over</li><li>Encourage them to use properties of functions and derivatives (zeros, max/mins etc) to speed up the process&nbsp;</li></ul><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/5dYPDyufV98Usf1E9E5eDGoYWxd6ZsNAQCKgB/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/5dYPDyufV98Usf1E9E5eDGoYWxd6ZsNAQCKgB/s320/EM_Downloads.png" width="320" /></a></div><ul><li>Derivative Match Cards (<a href="https://drive.google.com/open?id=1gz94qANBvz9ioNx2Y5HSqjzhV6LWYKyja_cX579Hm2c" target="_blank">Google Doc</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkU0R0ODVJTFIwLTQ" target="_blank">PDF</a>)</li><li>Derivative Match Teacher Key (<a href="https://drive.google.com/open?id=0B9algQOOR_bkUTlpcnBtUFhET0k" target="_blank">PDF</a>)</li><li>Desmos CardSort <a href="https://teacher.desmos.com/activitybuilder/custom/57b342ce867e43be309e0451" target="_blank">version</a></li><li>For an online version (Flash based) try out <a href="http://www.maa.org/sites/default/files/images/upload_library/47/Margolius/matchinggame.html" target="_blank">this link</a> from the MAA. Thanks to <a href="https://twitter.com/EulersNephew/status/739917206922756096" target="_blank">@EulersNephew</a> for pointing this out</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks&nbsp;</span><br /><br />David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com3tag:blogger.com,1999:blog-7366940278418424797.post-16381242534224350132016-04-04T14:58:00.000-04:002016-04-05T10:10:34.091-04:00Rate of Change Continuum <a href="https://1.bp.blogspot.com/-qfMY8u3wmlA/VwKJY7sudeI/AAAAAAAABBw/ULBA7KqneDUKT6FRReX0SmGdEJBKw8iyQ/s1600/RoC-Continuum.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-qfMY8u3wmlA/VwKJY7sudeI/AAAAAAAABBw/ULBA7KqneDUKT6FRReX0SmGdEJBKw8iyQ/s320/RoC-Continuum.JPG" width="320" /></a>A continuum is something where the level difficulty increases in incremental steps. In this case the continuum is dealing with calculating the rate of change (slope) of a linear relationship.<br />We have previously posted a continuum for solving equations <a href="http://engaging-math.blogspot.ca/2015/05/9-applied-solving-equations-continuum.html" target="_blank">here</a> and <a href="http://engaging-math.blogspot.ca/2015/05/9-academic-solving-equations-continuum.html" target="_blank">here</a> but this one is a bit different. This one has five levels of determining the rate of change from a graph (in context) for a linear relationship. The first level shows lattice points, a rate triangle and the calculation of both rise and run (super basic) and the difficulty increases with each level (see below) until the last level where there is only a scale with no grid lines (so the answer is more of an estimate).<br /><a href="https://1.bp.blogspot.com/-jj2PlMKHvuA/VwKMw2GO6FI/AAAAAAAABB8/P7nZdfQfhPAp1YB4VjZmQzgV4XdadfH8A/s1600/RateofChangeUV.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://1.bp.blogspot.com/-jj2PlMKHvuA/VwKMw2GO6FI/AAAAAAAABB8/P7nZdfQfhPAp1YB4VjZmQzgV4XdadfH8A/s320/RateofChangeUV.gif" width="320" /></a><br />Each page has 6 graphs and students (once they choose the level to start with) choose to answer any three. If they do so correctly then they can move to the next level. The To make things a bit more fun, rather than check the answers with you, we suggest using a UV pen and ink written on the question cards for students to check.<br />This activity is probably best meant as a consolidation. Note that the expectation is about investigating so hopefully students will have had a chance to develop their own strategies for determining the rate of change. This activity just helps to scaffold it a bit in case they are having trouble (Eg a common mistake that students make when determining the rate of change when the line is in context is to just count boxes for the rise and run without considering the scale).<br />Note that we also have an <a href="http://explaineverything.com/" target="_blank">Explain Everything</a> version if you have students who have iPads (you may even want to try out the new Explain Everything<a href="http://explaineverything.com/news/worldwide-launch-of-explain-everything-collaborative-whiteboard/" target="_blank"> Collaborative Whiteboard</a> app to have students work in groups from different devices).<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-rPnSEU09DOU/VwKt_HRtSrI/AAAAAAAABCk/GqtbUlXE_AMW7_tUaIAke8tlBvMnxskbA/s1600/GraphicalRateContinuum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-rPnSEU09DOU/VwKt_HRtSrI/AAAAAAAABCk/GqtbUlXE_AMW7_tUaIAke8tlBvMnxskbA/s640/GraphicalRateContinuum.png" width="560" /></a></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMUK3F6JvwwYsoPVlleNoPMPA/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMUK3F6JvwwYsoPVlleNoPMPA/s320/EM_Curriculum.png" width="320" /></a></div><ul><li>MPM1D, MFM1P - determine, through investigation, connections among the representations of a constant rate of change of a linear relation.</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyYRnSRf9G0BWQzZIyZ0kBKJg/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyYRnSRf9G0BWQzZIyZ0kBKJg/s320/EM_Materials.png" width="320" /></a></div><ul><a href="https://4.bp.blogspot.com/-kArqFHvxJJs/VwKtwDTt4OI/AAAAAAAABCg/GDx8Q0Ve-2w9pivOU59Qc-OFnjingV-bA/s1600/GraphicalRateContinuum-page.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-kArqFHvxJJs/VwKtwDTt4OI/AAAAAAAABCg/GDx8Q0Ve-2w9pivOU59Qc-OFnjingV-bA/s320/GraphicalRateContinuum-page.png" width="225" /></a><li>20 copies of each of the question cards in different colour cardstock for each level, &nbsp;laminated (use colours that allow seeing the magic pen writing). Note that you may not need 20 copies of each. Perhaps fewer of the first couple levels and last level as most kids will probably be starting in the 2nd or 3rd level</li><li>3 sets of the answer cards (use magic pen to write the answers anywhere along each equation, they could be sideways, upside-down, (the answers are on the last page of the Google Doc). To help distinguish the answer cards to the question cards you should put a stamp or sticker on the back.</li><li>3 "magic" pens can be purchased at&nbsp;<a href="http://www.chapters.indigo.ca/en-ca/house-and-home/secret-message-writing-set/5037200004502-item.html?ikwid=secret+message+writing&amp;ikwsec=Home&amp;ikwidx=0" target="_blank">Chapters/Indigo</a>&nbsp;or we found these at a Scholastic's book fair. We have since purchased some on&nbsp;<a href="http://www.ebay.ca/sch/i.html?_odkw=uv+pen&amp;_osacat=0&amp;_from=R40&amp;_trksid=p2045573.m570.l1313.TR0.TRC0.H0.Xuv+invisible+pen.TRS0&amp;_nkw=uv+invisible+pen&amp;_sacat=0" target="_blank">eBay</a>.</li></ul><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-lGro3asxop4/VUj5VAiy0HI/AAAAAAAAAj4/dBAlRjl21SQocxZZq62H0SMqjRwvCEHhw/s1600/UVpens.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-lGro3asxop4/VUj5VAiy0HI/AAAAAAAAAj4/dBAlRjl21SQocxZZq62H0SMqjRwvCEHhw/s320/UVpens.png" width="550" /></a></div><div><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GUXs6H98qhhtk0P6vXRp9USQ/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GUXs6H98qhhtk0P6vXRp9USQ/s320/EM_Procedure.png" width="320" /></a></div><ol><a href="https://1.bp.blogspot.com/-VDpctyJ8arc/VwKyCFSUMeI/AAAAAAAABC4/IB9w_8PDJIkJ7CgwrBOt4uZAcGLmNTGrQ/s1600/RateContinuumEE.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-VDpctyJ8arc/VwKyCFSUMeI/AAAAAAAABC4/IB9w_8PDJIkJ7CgwrBOt4uZAcGLmNTGrQ/s320/RateContinuumEE.PNG" width="320" /></a><li>For this activity to be successful, students must start at the appropriate envelope. If they start in one that is too hard they will be frustrated and if they start in one that is too easy they will be bored. Use an exit card (the day before) to help you decide which envelope each student should start in. When given back the exit card write down the level they will start in.&nbsp;</li><li>Place the questions in piles in order of difficulty and set up three stations for the answer cards. Students will get a card and answer any 3 questions.&nbsp;</li><li>To check their answers, they will go to a station and use the magic pens. Students may decide to do one question at a time and then go check their answer or they may do all 3 and then check. Students are monitoring themselves so they decide. If they get the first 3 right, they have a level of mastery to move themselves to the next level. If not there are more questions on the card until they master that type.&nbsp;</li><li>As they move through the continuum, the hope is that they reach level 4 which matches the grade 9 curriculum. Since our goal is to get them to level 4, students should solve ALL equations on that card instead of just three.&nbsp;</li><li>The fifth level is set up to challenge students who are moving forward quickly. They should solve all questions on this card. They require some estimation and so answers that students get should be approximate.&nbsp;</li></ol><div><b>Note</b> that for the Explain Everything version, there are still 6 possible graphs for each level but only two on each page. And to check the answer, slide the black ellipse to either the bottom left or right corner.&nbsp;</div><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHMjKEyZYjeqDgtT3LS64ZmAw/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHMjKEyZYjeqDgtT3LS64ZmAw/s320/EM_Downloads.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"></div><ul><li>Graphical Rate Continuum (<a href="https://drive.google.com/open?id=14ZfL7W5ZX0Mr4Ma6Gb7oVs1AHf0BLxYHu9HVCKL1YrU" target="_blank">Google Doc</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkV0ExcW5UQTJWUDg" target="_blank">PDF</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkemNLLWMtaHVjSFU" target="_blank">Explain Everything</a>)</li><li>Entire <a href="https://drive.google.com/open?id=0B9algQOOR_bkdlRYY2J2bGlqek0" target="_blank">Folder</a></li></ul><div class="separator" style="clear: both; text-align: left;"><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span></div>David Petrohttp://www.blogger.com/profile/16551690042242217798noreply@blogger.com1tag:blogger.com,1999:blog-7366940278418424797.post-71045375806802990092016-02-28T21:53:00.000-05:002016-03-21T23:06:26.984-04:00Geometer's Sketchpad - Trig Ratio Generator<div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="https://3.bp.blogspot.com/-2zwLzz_U7Ug/VtOw4PMf2CI/AAAAAAAAA28/YwWBO8EPm3Y/s1600/GSP-TrigGenerator2.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="236" src="https://3.bp.blogspot.com/-2zwLzz_U7Ug/VtOw4PMf2CI/AAAAAAAAA28/YwWBO8EPm3Y/s320/GSP-TrigGenerator2.png" width="320" /></a><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;">When using the Geometer's Sketchpad (for both computer and iPad) it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).</span><br /><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;"><span style="font-size: 14.85px; line-height: 20.79px;">In this activity, students can practice two very specific skills dealing with trigonometry. The first is simply being able to correctly place the names of the sides of a right triangle (opposite, adjacent and hypotenuse). Students drag the side names and then can check their answers and then randomly generate another triangle to try again. The second is one where a random triangle is generated that shows information about two sides and one angle. Students then drag parts of an equation to create a trig ratio equation. They can check their answer and then randomly generate other right angled triangle to try again.&nbsp;</span></span><br /><div>This is not meant to be something that a student uses for a long length of time but instead just some quick practice to re enforce the basic ideas from trig ratios.<br /><div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><ul><a href="https://3.bp.blogspot.com/-tPRGbeqBkmA/VtOxCKwDdzI/AAAAAAAAA3A/aI_EfI7GdeI/s1600/GSP-TrigGenerator1.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="237" src="https://3.bp.blogspot.com/-tPRGbeqBkmA/VtOxCKwDdzI/AAAAAAAAA3A/aI_EfI7GdeI/s320/GSP-TrigGenerator1.png" width="320" /></a><li>MFM2P, MPM2D - determine, through investigation (e.g., using dynamic geometry software, concrete materials), the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios.</li><li>MCR3U, MCF3M, MBF3C - As review</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul style="background-color: white; color: #6a6a6a; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px; margin: 0.5em 0px; padding: 0px 2.5em;"><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">All that is needed is the electronic download (below)</li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">Note that this really works well on an iPad using the&nbsp;<a href="https://itunes.apple.com/ca/app/sketchpad-explorer/id452811793?mt=8" style="color: #7ba2d3; text-decoration: none;" target="_blank">Sketchpad Explorer App</a>&nbsp;(which is free)</li><li>You can also use this on any web based computer (or Chromebook) with this&nbsp;<span style="color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;"><a href="http://mail.wecdsb.on.ca/~david_petro/WebSketches/TrigGenerator/index.html" target="_blank">Web&nbsp;sketch</a></span></li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;">Watch the video below to see how to use the sketch</span><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/-LArGsB2N8o/0.jpg" frameborder="0" height="315" src="https://www.youtube.com/embed/-LArGsB2N8o?feature=player_embedded" width="530"></iframe></div><br /><div class="separator" style="clear: both; text-align: left;"></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul style="background-color: white; color: #6a6a6a; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px; margin: 0.5em 0px; padding: 0px 2.5em;"><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">TrigGenerator.gsp (<a href="http://mail.wecdsb.on.ca/~david_petro/sketches/TrigGenerator.gsp" style="color: #7ba2d3; text-decoration: none;" target="_blank">iPad/V5</a>)</li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px;">Web&nbsp;sketch&nbsp;</span><a href="http://mail.wecdsb.on.ca/~david_petro/WebSketches/TrigGenerator/index.html" style="color: #7ba2d3; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px; text-decoration: none;" target="_blank">here</a></li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">For more sketches like this go to my&nbsp;<a href="http://mail.wecdsb.on.ca/~david_petro/sketches/Sketches.htm" style="color: #7ba2d3; text-decoration: none;" target="_blank">full page</a></li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15.5556px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span></div>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-58785047098368398242016-02-19T16:01:00.000-05:002016-07-16T18:58:34.119-04:00Number Sentences Sort (update)<div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="https://2.bp.blogspot.com/-u_MnWeccgsw/Vsdgg5e7VBI/AAAAAAAAA1w/SQ5mTB4FjA8/s1600/NumberSentence.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-u_MnWeccgsw/Vsdgg5e7VBI/AAAAAAAAA1w/SQ5mTB4FjA8/s320/NumberSentence.JPG" width="320" /></a>One of the smaller expectations we have to deal with is the ability for students to interpret algebraic equations. You know: "what does 2x&nbsp;+ 1 mean"?. We created this very simple sorting activity where students are given expressions (and equations) and the sentence to describe them and have to match them up. This is meant to be an activity that is relatively quick. We have two versions here. One for grade 7 that only has expressions and one for grade 8 that has equations as well. We also have an <a href="http://explaineverything.com/" target="_blank">Explain Everything</a> version of each so that if you have an iPad (or Chromebook), with that app, you can have your students sort them electronically. This can also be used as review in Grade 9.<br /><b>Note:</b> This is an update to the same activity posted <a href="http://engaging-math.blogspot.ca/2015/04/connecting-words-and-algebraic.html" target="_blank">last year but</a> now with a grade 8 and Explain Everything version<br /><a href="https://1.bp.blogspot.com/-H6Go25Y6TZ4/V4q7jxLVraI/AAAAAAAABWw/RKLJczP5u0AaYLXjxhRFvXzcAIgmn6GyACLcB/s1600/DesmosCardsort.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="208" src="https://1.bp.blogspot.com/-H6Go25Y6TZ4/V4q7jxLVraI/AAAAAAAABWw/RKLJczP5u0AaYLXjxhRFvXzcAIgmn6GyACLcB/s320/DesmosCardsort.jpg" width="320" /></a><b>Double Note:</b> This has been updated again to now include a Desmos card sort. So both card sorts are now transferred to this new Desmos feature. You can learn about Desmos Card Sorts by clicking <a href="http://learn.desmos.com/cardsort" target="_blank">here</a>. Download the Teacher versions (which you can copy) of these activities below in the download section.<br /><div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><ul><li>Gr7PA - translate phrases describing simple mathematical relationships into algebraic expressions using concrete materials</li><li>Gr8PA - translate statements describing mathematical relationships into algebraic expressions and equations</li><li>MPM1D, MFM1P - As review</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><a href="https://4.bp.blogspot.com/--Ng84l2DJko/Vsdln1nCorI/AAAAAAAAA2E/1A3DDhih0PU/s1600/NumberSentences.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="210" src="https://4.bp.blogspot.com/--Ng84l2DJko/Vsdln1nCorI/AAAAAAAAA2E/1A3DDhih0PU/s320/NumberSentences.png" width="320" /></a><li>For the grade 7 version there are four different (but similar) sets. One set per page. For the grade 8 version there are three different (but similar) sets. One set per page.&nbsp;</li><li>Print each page on card stock (we also suggest laminating). We suggest that each set be printed on different colour card stock for easy sorting. Cut each out and put each set in an envelope.</li><li>Obviously you will have to decide how many sets you will need for your class depending on whether you pair students up or not.&nbsp;</li><li>Note that in the version with equations, there are some algebraic expressions that do not have matching sentences. In these cases, students will have to write their own.</li><li>If you choose to use the Explain Everything version, then you probably want to download that .xpl file and put it on a server where your students can get easy access to it.&nbsp;</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-VIut__CRro8/Vsd-2YMxeXI/AAAAAAAAA2Y/fn3Nbj0LOVA/s1600/NumberSentencesEE.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://3.bp.blogspot.com/-VIut__CRro8/Vsd-2YMxeXI/AAAAAAAAA2Y/fn3Nbj0LOVA/s320/NumberSentencesEE.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Explain Everything Screenshot</td></tr></tbody></table><ol><li>Depending on how many students you have you may want to do this individually, in pairs or in larger groups. The activity is not super complex so we don't recommend anything bigger than pairs.&nbsp;</li><li>Students take each set and sort the algebraic expression with the written version.&nbsp;</li><li>When they are done their set they can trade with another group that has a different colour of cards. If they are using the Explain Everything version then they can just go to the next slide.&nbsp;</li><li>There is a homework sheet for consolidation that includes both expressions and equations as well.</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul><li>NumberSentences-Expressions (<a href="https://drive.google.com/open?id=0B9algQOOR_bkQWszeE9qa0d0cEU" target="_blank">doc</a>. <a href="https://drive.google.com/open?id=0B9algQOOR_bkMHpmM3lUbFNGbHc" target="_blank">PDF</a>, <a href="http://www.edutopia.org/practice/steam-project-based-learning-real-solutions-driving-questions" target="_blank">XPL</a>, <a href="https://teacher.desmos.com/activitybuilder/custom/578a780c861c7b82316ed2d9" target="_blank">Desmos</a>)</li><li>NumberSentences-Equations (<a href="https://drive.google.com/open?id=0B9algQOOR_bkdDl6U3Fzbm1QOVE" target="_blank">doc</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkQ2N1MnI4dXlvMVE" target="_blank">PDF</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkT1ptcGJJRnMzYXM" target="_blank">XPL</a>, <a href="https://teacher.desmos.com/activitybuilder/custom/578a839d2458b548194bdb75" target="_blank">Desmos</a>)</li><li>NumberSentencesHomework-Equations (<a href="https://drive.google.com/open?id=0B9algQOOR_bkWVZMMUVwSTY2d1U" target="_blank">doc</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkV3prQ2dBNUdrN0E" target="_blank">PDF</a>)</li><li>Entire <a href="https://drive.google.com/open?id=0B9algQOOR_bkRmRZTmJXemdIV0E" target="_blank">Folder</a></li></ul><div><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span></div>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-50952453640908968462016-01-30T23:50:00.000-05:002016-02-19T15:55:45.840-05:00Row Games<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://4.bp.blogspot.com/-yPlSNaP-Y6U/Vq2KO_5SUrI/AAAAAAAAA0I/LlaU4cBVyLg/s1600/RowGame.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-yPlSNaP-Y6U/Vq2KO_5SUrI/AAAAAAAAA0I/LlaU4cBVyLg/s320/RowGame.png" width="231" /></a>We saw this activity in 2010 when I first found&nbsp;<complete id="goog_600986540"><a href="https://twitter.com/k8nowak" target="_blank">@K8Nowak</a>'s blog <a href="http://function-of-time.blogspot.ca/" target="_blank">f(t)</a>. I don't know if I would call a <a href="http://function-of-time.blogspot.ca/2009/12/row-games-galore.html" target="_blank">Row Game</a> a particularly engaging activity but I am convinced that any way we can make doing boring homework questions more palatable for students is a good thing. The premiss is that you pair students up and they get a worksheet of questions. The questions are in two columns. Each person does one column and if they have done things correctly then their questions on the same row should have the same answer. If they don't then either one or both of them are incorrect and they have to work together to get the correct answer. So this is a self checking activity. We made a bunch of them at the time and I just stumbled upon them this week so we thought&nbsp;</complete>we would post them. These ones are for ratios, proportion, simplifying expressions and solving simple equations.<br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div>MFM1P, MPM1D<br /><div class="p1"></div><ul><li>illustrate equivalent ratios, using a variety of tools</li><li>solve for the unknown value in a proportion, using a variety of methods&nbsp;</li><li>make comparisons using unit rates</li><li>solve problems involving ratios, rates, and directly proportional relationships in various contexts, using a variety of methods</li><li>solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms</li><li>add and subtract polynomials involving the same variable up to degree three, using a variety of tools</li><li>multiply a polynomial by a monomial involving the same variable to give results up to degree three</li><li>solve first-degree equations with non fractional (Applied only) coefficients, using a variety of tools and strategies</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><li>&nbsp;Just the handouts (see below)</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><ol><li>Pair students up</li><li>Have students decide who will be Student A&nbsp;or Student B, and have them complete Problem Set A or B.</li><li>The answers in each row should match. If they do not match, work together to determine the correct answer.</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul><li>See the files in one folder <a href="https://drive.google.com/folderview?id=0B9algQOOR_bkZkJkRkpJVVRJZzg&amp;usp=sharing" target="_blank">here</a></li><li>Proportions (<a href="https://drive.google.com/open?id=0B9algQOOR_bkTy1lN1ZVUHgzOHc" target="_blank">Word</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkZExlSEpvcWpseEk" target="_blank">PDF</a>)</li><li>Proportions Review (<a href="https://drive.google.com/open?id=0B9algQOOR_bkRDRKbGNkb1BWM1k" target="_blank">Word</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkVDVURFZZSkt3LW8" target="_blank">PDF</a>)</li><li>Simplifying Expressions (<a href="https://drive.google.com/open?id=0B9algQOOR_bkN2s3QkQ1Y05HTjA" target="_blank">Word</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkcU1NV0owSXdrdGc" target="_blank">PDF</a>)</li><li>Adding Polynomials (<a href="https://drive.google.com/open?id=0B9algQOOR_bkMUJ5aWJOQ3NmdlE" target="_blank">Word</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkYXVDVzlXWklLeTQ" target="_blank">PDF</a>)</li><li>Simplifying Expressions with Multiplication (<a href="https://drive.google.com/open?id=0B9algQOOR_bkS2FublBoVW9HT0E" target="_blank">Word</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkWDA3NVpIUjVQR2M" target="_blank">PDF</a>)</li><li>Solving Equations (<a href="https://drive.google.com/open?id=0B9algQOOR_bkRWxPdk8wbGFQTDg" target="_blank">Word</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkVWFienhwY2xIV2c" target="_blank">PDF</a>)</li><li>Solving Multistep Equations (<a href="https://drive.google.com/open?id=0B9algQOOR_bkMzd2Y3hOUy1scEk" target="_blank">Word</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkOVFnNmdTazV3RVk" target="_blank">PDF</a>)</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span><br /><br />David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-50498971837063082872016-01-25T11:15:00.001-05:002016-01-25T11:15:37.268-05:00Grade 11 Exam Review Tower Challenge<div class="separator" style="clear: both;"><a href="http://4.bp.blogspot.com/-ehmqlmSdzho/U6mh5vR8FGI/AAAAAAAAAAs/rCG4Ek5aCkE/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-ehmqlmSdzho/U6mh5vR8FGI/AAAAAAAAAAs/rCG4Ek5aCkE/s320/EM_Activity.png" width="320" /></a></div><div class="separator" style="clear: both;"><a href="http://3.bp.blogspot.com/-4ZCxJFGlX_c/VnhYNRJzVeI/AAAAAAAAAVY/8lCCoLDx5lg/s1600/ScreenHunter_03%2BDec.%2B21%2B14.49.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="248" src="http://3.bp.blogspot.com/-4ZCxJFGlX_c/VnhYNRJzVeI/AAAAAAAAAVY/8lCCoLDx5lg/s320/ScreenHunter_03%2BDec.%2B21%2B14.49.jpg" width="320" /></a>This is a review activity on many of the topics found in grade 11 university where students answer questions and are rewarded with building materials for each correct answer. The building materials (spaghetti &amp; marshmallows) are then used with the goal being the creation of tallest tower. This is based originally on a TIPS activity on quadratics for MBF3C (<a href="http://www.edugains.ca/resources/LearningMaterials/TIPS/tips4rm/mbf3c/Unit3_QuadraticsPart1.doc" target="_blank">Unit 3, Day 6</a>). &nbsp;</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="http://1.bp.blogspot.com/-gghZgvdK6dY/U6mh58SBv3I/AAAAAAAAABQ/UO2HWN5iTKg/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://1.bp.blogspot.com/-gghZgvdK6dY/U6mh58SBv3I/AAAAAAAAABQ/UO2HWN5iTKg/s320/EM_Curriculum.png" width="320" /></a></div><div class="separator" style="clear: both;">MCR3U&nbsp;</div><div class="p1"></div><ul><li>demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations;</li><li>determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real<span class="s1">-</span>world applications;</li><li>demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.</li><li>evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways;</li><li>identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real<span class="s1">-</span>world applications.</li><li>demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems;</li><li>make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities.</li><li>determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;</li><li>demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;</li><li>identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real<span class="s1">-</span>world applications.</li></ul><div class="separator" style="clear: both;"><a href="http://3.bp.blogspot.com/-4ZOgYr6m5kI/U6mh6ZwEiTI/AAAAAAAAAA8/v31FH_JQMBE/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://3.bp.blogspot.com/-4ZOgYr6m5kI/U6mh6ZwEiTI/AAAAAAAAAA8/v31FH_JQMBE/s320/EM_Materials.png" width="320" /></a></div><div class="separator" style="clear: both;"></div><ul><a href="http://2.bp.blogspot.com/-I3S0SdmZTtw/VqWxjUmIA5I/AAAAAAAAAzY/XABuOTDJa2E/s1600/Gr11TowerQuestion.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://2.bp.blogspot.com/-I3S0SdmZTtw/VqWxjUmIA5I/AAAAAAAAAzY/XABuOTDJa2E/s200/Gr11TowerQuestion.png" width="150" /></a><li>1 bag of spaghetti and 1-2 bags of small marshmallows (or 1 box of straws and 1-inch pieces of tape) &nbsp;</li><li>a question sheet for each student</li><li>a teacher answer sheet&nbsp;</li><li>Optional - a whiteboard for each student to work out their solutions</li><li>Optional - prize for the group with the tallest tower</li></ul><div class="separator" style="clear: both;"><a href="http://2.bp.blogspot.com/-HPJo5aQvTFk/U6mh6pmYYRI/AAAAAAAAABA/udTzAA2E7K8/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-HPJo5aQvTFk/U6mh6pmYYRI/AAAAAAAAABA/udTzAA2E7K8/s320/EM_Procedure.png" width="320" /></a></div><ol><a href="http://4.bp.blogspot.com/-AuDPUDWwjQw/VqWxreYsUrI/AAAAAAAAAzg/IalzivBL8v0/s1600/Gr11TowerAnswer.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-AuDPUDWwjQw/VqWxreYsUrI/AAAAAAAAAzg/IalzivBL8v0/s320/Gr11TowerAnswer.png" width="272" /></a><li>Place students in groups (ideally no bigger than 3 per group)</li><li>Hand out question sheets (and optional whiteboards) to each student.</li><li>Have students answer questions from their sheet in any order they want. For every correct answer they will get some building materials (eg: 2 spagetti &amp; 3 marshmallows, the amount of each reward is indicated on the student question sheet ). The harder the question the more materials they will get. Eventually the building materials will be used to create a tower with the goal to create the tallest free standing tower.</li><li>Students work in groups to answer the questions and bring their solutions up to you to be checked. Only one member from each group can come up at a time. Each group can answer&nbsp;each question only once. To keep track of this, use the teacher answer sheet to check off&nbsp;which questions each group has answered as they come up.</li><li>Leave about 20 min at the end of the class for students to create their towers (students can no longer answer questions)</li><li>Take lots of pictures and celebrate the group with the tallest free standing tower.</li></ol><div class="separator" style="clear: both;"><a href="http://2.bp.blogspot.com/--u_iZ8uGCaU/U6mh69-EDiI/AAAAAAAAABM/ZvL78awLElA/s1600/EM_SampleWork.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/--u_iZ8uGCaU/U6mh69-EDiI/AAAAAAAAABM/ZvL78awLElA/s320/EM_SampleWork.png" width="320" /></a></div><div style="text-align: center;"><iframe allowfullscreen="true" frameborder="0" height="389" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1xTOs38LhgmFIJft4sVZ26AtausakVw-pMuxbaamaAEA/embed?start=true&amp;loop=true&amp;delayms=3000" webkitallowfullscreen="true" width="480"></iframe></div><div class="separator" style="clear: both;"><a href="http://2.bp.blogspot.com/-L7w-qdo7fqs/U6mh59rcVBI/AAAAAAAAAA0/qex7yDhAr7Y/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-L7w-qdo7fqs/U6mh59rcVBI/AAAAAAAAAA0/qex7yDhAr7Y/s320/EM_Downloads.png" width="320" /></a></div><div><ul><li>Gr11UTowerChallengeExamReview (with answer sheet) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkZFhfWUZ2ZzJDTUU" target="_blank">pdf</a>,&nbsp;<a href="https://drive.google.com/open?id=0B9algQOOR_bkVGRIVmNqUHdrZGM" target="_blank">doc</a>)</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span></div>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-76209457751572597022015-12-21T20:05:00.000-05:002016-07-04T10:46:33.696-04:00Simplifying Expressions and Solving Equations Tower Challenge<div class="separator" style="clear: both;"><a href="http://4.bp.blogspot.com/-ehmqlmSdzho/U6mh5vR8FGI/AAAAAAAAAAs/rCG4Ek5aCkE/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-ehmqlmSdzho/U6mh5vR8FGI/AAAAAAAAAAs/rCG4Ek5aCkE/s320/EM_Activity.png" width="320" /></a></div><div class="separator" style="clear: both;"><a href="http://3.bp.blogspot.com/-4ZCxJFGlX_c/VnhYNRJzVeI/AAAAAAAAAVY/8lCCoLDx5lg/s1600/ScreenHunter_03%2BDec.%2B21%2B14.49.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="248" src="https://3.bp.blogspot.com/-4ZCxJFGlX_c/VnhYNRJzVeI/AAAAAAAAAVY/8lCCoLDx5lg/s320/ScreenHunter_03%2BDec.%2B21%2B14.49.jpg" width="320" /></a>This is a review activity on simplifying expressions and solving equations for grade 9 applied where students answer questions and are rewarded with building materials for each correct answer. The building materials (spagetti &amp; marshmallows) are then used with the goal being the creation of tallest tower. This is based originally on a TIPS activity on quadratics for MBF3C (<a href="http://www.edugains.ca/resources/LearningMaterials/TIPS/tips4rm/mbf3c/Unit3_QuadraticsPart1.doc" target="_blank">Unit 3, Day 6</a>). &nbsp;We have a similar activity for grade 9 academic that can be found <a href="http://engaging-math.blogspot.com/2015/12/number-sense-and-algebra-tower-challenge.html" target="_blank">here</a>.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="http://1.bp.blogspot.com/-gghZgvdK6dY/U6mh58SBv3I/AAAAAAAAABQ/UO2HWN5iTKg/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-gghZgvdK6dY/U6mh58SBv3I/AAAAAAAAABQ/UO2HWN5iTKg/s320/EM_Curriculum.png" width="320" /></a></div><div class="separator" style="clear: both;">MPM 1P</div><ul><li>substitute into and evaluate algebraic expressions involving exponents&nbsp;</li><li>describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three [i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional, can be represented by (x)(x) or x<sup>2</sup>; volume, which is three dimensional,can be represented by (x)(x)(x), (x<sup>2</sup>)(x),or&nbsp;x<sup>3</sup>]</li><li>add and subtract polynomials involving the same variable up to degree three using a variety of tools</li><li>multiply a polynomial by a monomial involving the same variable to give results up to degree three using a variety of tools</li><li>solve first-degree equations with nonfractional coefficients, using a variety of tools</li><li>substitute into algebraic equations and solve for one variable in the first degree</li></ul><div class="separator" style="clear: both;"><a href="http://3.bp.blogspot.com/-4ZOgYr6m5kI/U6mh6ZwEiTI/AAAAAAAAAA8/v31FH_JQMBE/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://3.bp.blogspot.com/-4ZOgYr6m5kI/U6mh6ZwEiTI/AAAAAAAAAA8/v31FH_JQMBE/s320/EM_Materials.png" width="320" /></a></div><div class="separator" style="clear: both;"></div><ul><li>1 bag of spaghetti and 1-2 bags of small marshmallows (or 1 box of straws and 1-inch pieces of tape) &nbsp;</li><li>a question sheet for each student</li><li>a teacher answer sheet&nbsp;</li><li>Optional - a whiteboard for each student to work out their solutions</li><li>Optional - prize for the group with the tallest tower</li></ul><div class="separator" style="clear: both;"><a href="http://2.bp.blogspot.com/-HPJo5aQvTFk/U6mh6pmYYRI/AAAAAAAAABA/udTzAA2E7K8/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-HPJo5aQvTFk/U6mh6pmYYRI/AAAAAAAAABA/udTzAA2E7K8/s320/EM_Procedure.png" width="320" /></a></div><div class="separator" style="clear: both;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/--ITKeOXH3MA/Vnhcj07CBeI/AAAAAAAAAWs/v9owU7xPJE8/s1600/ScreenHunter_05%2BDec.%2B21%2B15.08.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br /></a></div><ol><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-tvK_CovFWJo/VnheJvO0MmI/AAAAAAAAAW4/kgQV0kJd4Og/s1600/ScreenHunter_02%2BDec.%2B21%2B14.44.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="197" src="https://1.bp.blogspot.com/-tvK_CovFWJo/VnheJvO0MmI/AAAAAAAAAW4/kgQV0kJd4Og/s200/ScreenHunter_02%2BDec.%2B21%2B14.44.jpg" width="200" /></a></div><a href="http://2.bp.blogspot.com/-RYx6KWq2Bmg/VnhePDTzYEI/AAAAAAAAAXE/fBbgovhLszw/s1600/ScreenHunter_05%2BDec.%2B21%2B15.08.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-RYx6KWq2Bmg/VnhePDTzYEI/AAAAAAAAAXE/fBbgovhLszw/s320/ScreenHunter_05%2BDec.%2B21%2B15.08.jpg" width="289" /></a><li>Place students in groups (ideally no bigger than 3 per group)</li><li>Hand out question sheets (and optional whiteboards) to each student.</li><li>Have students answer questions from their sheet in any order they want. For every correct answer they will get some building materials (eg: 2 spagetti &amp; 3 marshmallows, the amount of each reward is indicated on the student question sheet ). The harder the question the more materials they will get. Eventually the building materials will be used to create a tower with the goal to create the tallest free standing tower.</li><li>Students work in groups to answer the questions and bring their solutions up to you to be checked. Only one member from each group can come up at a time. Each group can answer&nbsp;each question only once. To keep track of this, use the teacher answer sheet to check off&nbsp;which questions each group has answered as they come up.</li><li>Leave about 20 min at the end of the class for students to create their towers (students can no longer answer questions)</li><li>Take lots of pictures and celebrate the group with the tallest free standing tower.</li></ol><br /><br /><div class="separator" style="clear: both;"><a href="http://2.bp.blogspot.com/--u_iZ8uGCaU/U6mh69-EDiI/AAAAAAAAABM/ZvL78awLElA/s1600/EM_SampleWork.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/--u_iZ8uGCaU/U6mh69-EDiI/AAAAAAAAABM/ZvL78awLElA/s320/EM_SampleWork.png" width="320" /></a></div><div style="text-align: center;"><iframe allowfullscreen="true" frameborder="0" height="389" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1xTOs38LhgmFIJft4sVZ26AtausakVw-pMuxbaamaAEA/embed?start=true&amp;loop=true&amp;delayms=3000" webkitallowfullscreen="true" width="480"></iframe></div><div class="separator" style="clear: both;"><a href="http://2.bp.blogspot.com/-L7w-qdo7fqs/U6mh59rcVBI/AAAAAAAAAA0/qex7yDhAr7Y/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-L7w-qdo7fqs/U6mh59rcVBI/AAAAAAAAAA0/qex7yDhAr7Y/s320/EM_Downloads.png" width="320" /></a></div><div><ul><li>Gr9AppliedSimplifyingExpression&amp;SolvingEquationsTowerChallengeQuestions (<a href="https://drive.google.com/file/d/0B6mniFHBcF1nc3k5ZGtIbnJRQ0U/view?usp=sharing" target="_blank">pdf</a>,&nbsp;<a href="https://drive.google.com/file/d/0B6mniFHBcF1ncUZQa2NxQmRBSkE/view?usp=sharing" target="_blank">doc</a>)</li><li>Gr9AppliedSimplifyingExpression&amp;SolvingEquationTowerChallengeTeacherAnswerSsheet (<a href="https://drive.google.com/file/d/0B6mniFHBcF1nNE10Y3psWmdnWHM/view?usp=sharing" target="_blank">pdf</a>,&nbsp;<a href="https://drive.google.com/file/d/0B6mniFHBcF1nSGhtSXJXcmVGU1U/view?usp=sharing" target="_blank">doc</a>)</li></ul><div><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span></div></div>GISELE JOBINhttps://plus.google.com/115554386495766205389noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-84706364181247664472015-12-20T11:47:00.001-05:002015-12-20T11:47:10.191-05:00Solving Equations Balance Method Card Sort<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://4.bp.blogspot.com/-Lcq44JCCG9A/VnbE6RlanOI/AAAAAAAAAyU/r9sOSh_JNsQ/s1600/Balance%2BMethod.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-Lcq44JCCG9A/VnbE6RlanOI/AAAAAAAAAyU/r9sOSh_JNsQ/s320/Balance%2BMethod.JPG" width="320" /></a>This is a simple activity where students are given a set of cards that represent the steps to take the given equation and use the balance method to solve it. The equations are relatively simple with most being two step solutions. This is not meant to be a big activity but just a warm up or perhaps something to do in the middle of class to break it up. There are 9 equations that can be solved so you could put students in groups or make multiple sets and have them work on them individually<br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><ul><a href="http://2.bp.blogspot.com/-O3EEkOdSD-k/VnbIHMF-bQI/AAAAAAAAAyg/1vyVqRFElOE/s1600/BalanceMethod1.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="195" src="http://2.bp.blogspot.com/-O3EEkOdSD-k/VnbIHMF-bQI/AAAAAAAAAyg/1vyVqRFElOE/s320/BalanceMethod1.png" width="320" /></a><li>Gr8PA - solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection, guess and check, and a “balance” model</li><li>MPM1D, MFM1P - solve first-degree equations, including equations with fractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies)</li></ul><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><a href="http://4.bp.blogspot.com/-caYOBVhQkAk/VnbJU5dNwYI/AAAAAAAAAy0/9z47MXpdTr8/s1600/BalanceMethod2.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-caYOBVhQkAk/VnbJU5dNwYI/AAAAAAAAAy0/9z47MXpdTr8/s320/BalanceMethod2.png" width="318" /></a><li>There are 9 sets of cards to print out and cut. We suggest printing on card stock and laminating. To help, each card will have it's set number just in case you mix up the cards. If you wish to use this with individual students rather than in groups you will need to print out more than one full set.</li><li>NOTE - there are two versions. One with the traditional adding and subtracting of terms on the same line and the other with the adding and subtracting of terms done below. Obviously choose the version you prefer. The equations are the same in both</li><li>We suggest putting each set in it's own envelop or zip-lock bag.&nbsp;</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><br /><ol><li>Randomly distribute the envelopes to groups (or individual students).&nbsp;</li><li>Have students use all the cards to show the steps to solve their question</li><li>Students should check their answer on paper or portable whiteboard</li><li>Once all groups (students) have correctly sorted their cards, they can exchange their set with the next group (since the sets are numbered they can just get the next numbered set - if they have set 1 then pass it to the group with set 2 etc).&nbsp;</li><li>This could be done 9 times or stopped when ever you wish.</li></ol><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><br /><ul><li>Solving Equations Card Sort Horizontal (<a href="https://drive.google.com/open?id=0B9algQOOR_bkT2l4aWtnMUhJeGc" target="_blank">pdf</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkelpRZ2JrYVNFTnc" target="_blank">doc</a>)</li><li>Solving Equations Card Sort Vertical (<a href="https://drive.google.com/open?id=0B9algQOOR_bkc3czeWUzTjZMWlU" target="_blank">pdf</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkNnJkQlBFNENmOVU" target="_blank">doc</a>)</li></ul><br /><span style="background-color: white; color: #6a6a6a; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-53791148424351473342015-12-18T14:56:00.000-05:002015-12-21T22:55:44.424-05:00Number Sense and Algebra Tower Challenge<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-ehmqlmSdzho/U6mh5vR8FGI/AAAAAAAAAAs/rCG4Ek5aCkE/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-ehmqlmSdzho/U6mh5vR8FGI/AAAAAAAAAAs/rCG4Ek5aCkE/s320/EM_Activity.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-hUMg8C-PjjY/VnRceFkDtfI/AAAAAAAAAT0/Y6HdL1Euc2E/s1600/ScreenHunter_04%2BDec.%2B18%2B14.19.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="260" src="http://2.bp.blogspot.com/-hUMg8C-PjjY/VnRceFkDtfI/AAAAAAAAAT0/Y6HdL1Euc2E/s320/ScreenHunter_04%2BDec.%2B18%2B14.19.jpg" width="320" /></a>This is a review activity on number sense and algebra for grade 9 academic where students answer questions and are rewarded with building materials for each correct answer. The building materials (spagetti &amp; marshmallows) are then used with the goal being the creation of tallest tower. This is based originally on a TIPS activity on quadratics for MBF3C (<a href="http://www.edugains.ca/resources/LearningMaterials/TIPS/tips4rm/mbf3c/Unit3_QuadraticsPart1.doc" target="_blank">Unit 3, Day 6</a>). &nbsp;We have a similar activity for grade 9 applied that can be found <a href="http://engaging-math.blogspot.ca/2015/12/simplifying-expressions-and-solving.html" target="_blank">here</a>.&nbsp;</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-gghZgvdK6dY/U6mh58SBv3I/AAAAAAAAABQ/UO2HWN5iTKg/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://1.bp.blogspot.com/-gghZgvdK6dY/U6mh58SBv3I/AAAAAAAAABQ/UO2HWN5iTKg/s320/EM_Curriculum.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">MPM 1D</div><ul><li>substitute into and evaluate algebraic expressions involving exponents</li><li>describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three [i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional, can be represented by (x)(x) or x<sup>2</sup>; volume, which is three dimensional,can be represented by (x)(x)(x), (x<sup>2</sup>)(x),or&nbsp;x<sup>3</sup>]</li><li>derive, through the investigation and examination of patterns, the exponent rules for multiplying and dividing monomials, and apply these rules in expressions involving one and two variables with positive exponents</li><li>extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents.</li><li>relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations</li><li>add and subtract polynomials with up to two variables</li><li>multiply a polynomial by a monomial involving the same variable</li><li>expand and simplify polynomial expressions involving one variable</li><li>solve first-degree equations, including equations with fractional coefficients, using a variety of tools</li><li>rearrange formulas involving variables in the first degree, with and without substitution</li><li>solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://3.bp.blogspot.com/-4ZOgYr6m5kI/U6mh6ZwEiTI/AAAAAAAAAA8/v31FH_JQMBE/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://3.bp.blogspot.com/-4ZOgYr6m5kI/U6mh6ZwEiTI/AAAAAAAAAA8/v31FH_JQMBE/s320/EM_Materials.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"></div><ul><li>1 bag of spaghetti and 1-2 bags of small marshmallows (or 1 box of straws and 1-inch pieces of tape) &nbsp;</li><li>a question sheet for each student</li><li>a teacher answer sheet&nbsp;</li><li>Optional - a whiteboard for each student to work out their solutions</li><li>Optional - prize for the group with the tallest tower</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-HPJo5aQvTFk/U6mh6pmYYRI/AAAAAAAAABA/udTzAA2E7K8/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-HPJo5aQvTFk/U6mh6pmYYRI/AAAAAAAAABA/udTzAA2E7K8/s320/EM_Procedure.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"></div><ol><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-cAoapA4huI8/VnQ54Tcnj4I/AAAAAAAAATI/JrrxlBEYNHQ/s1600/ScreenHunter_01%2BDec.%2B18%2B11.52.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://3.bp.blogspot.com/-cAoapA4huI8/VnQ54Tcnj4I/AAAAAAAAATI/JrrxlBEYNHQ/s200/ScreenHunter_01%2BDec.%2B18%2B11.52.jpg" width="199" /></a></div><a href="http://2.bp.blogspot.com/-2JUIB184TNI/VnRQTCwTfbI/AAAAAAAAATk/4MNjyr5cHnY/s1600/ScreenHunter_03%2BDec.%2B18%2B13.25.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-2JUIB184TNI/VnRQTCwTfbI/AAAAAAAAATk/4MNjyr5cHnY/s320/ScreenHunter_03%2BDec.%2B18%2B13.25.jpg" width="300" /></a><li>Place students in groups (ideally no bigger than 3 per group)</li><li>Hand out question sheets (and optional whiteboards) to each student.</li><li>Have students answer questions from their sheet in any order they want. For every correct answer they will get some building materials (eg: 2 spagetti &amp; 3 marshmallows, the amount of each reward is indicated on the student question sheet ). The harder the question the more materials they will get. Eventually the building materials will be used to create a tower with the goal to create the tallest free standing tower.</li><li>Students work in groups to answer the questions and bring their solutions up to you to be checked. Only one member from each group can come up at a time. Each group can answer each question only once. To keep track of this, use the teacher answer sheet to check off which questions each group has answered as they come up.</li><li>Leave about 20 min at the end of the class for students to create their towers (students can no longer answer questions)</li><li>Take lots of pictures and celebrate the group with the tallest free standing tower</li></ol><br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/--u_iZ8uGCaU/U6mh69-EDiI/AAAAAAAAABM/ZvL78awLElA/s1600/EM_SampleWork.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/--u_iZ8uGCaU/U6mh69-EDiI/AAAAAAAAABM/ZvL78awLElA/s320/EM_SampleWork.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div style="text-align: center;"><iframe allowfullscreen="true" frameborder="0" height="389" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1xTOs38LhgmFIJft4sVZ26AtausakVw-pMuxbaamaAEA/embed?start=true&amp;loop=true&amp;delayms=3000" webkitallowfullscreen="true" width="480"></iframe></div><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-L7w-qdo7fqs/U6mh59rcVBI/AAAAAAAAAA0/qex7yDhAr7Y/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-L7w-qdo7fqs/U6mh59rcVBI/AAAAAAAAAA0/qex7yDhAr7Y/s320/EM_Downloads.png" width="320" /></a></div><div style="text-align: left;"><ul><li>Gr9AcademicNumberSense&amp;AlgebraTowerChallengeQuestions (<a href="https://drive.google.com/file/d/0B6mniFHBcF1nV09MTGVtQTF1SDg/view?usp=sharing" target="_blank">pdf</a>, <a href="https://drive.google.com/file/d/0B6mniFHBcF1nMlBudWtvd3FlYXc/view?usp=sharing" target="_blank">doc</a>)</li><li>Gr9AcademicNumberSense&amp;AlgebraTowerChallengeTeacherAnswerSheet (<a href="https://drive.google.com/file/d/0B6mniFHBcF1nRG4tZEpXSXVPV2s/view?usp=sharing" target="_blank">pdf</a>, <a href="https://drive.google.com/file/d/0B6mniFHBcF1nOThxMWFMWTAzdms/view?usp=sharing" target="_blank">doc</a>)</li></ul><div><span style="background-color: white; color: #6a6a6a; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span></div></div>GISELE JOBINhttps://plus.google.com/115554386495766205389noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-16775937184961691702015-12-18T09:27:00.000-05:002015-12-18T09:27:32.918-05:00I Have, Who Has - Equations<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://3.bp.blogspot.com/-PXxXSSMurA4/VnLyMM0il8I/AAAAAAAAAxQ/X4J7002RGTg/s1600/IHaveWhoHas-Equations.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-PXxXSSMurA4/VnLyMM0il8I/AAAAAAAAAxQ/X4J7002RGTg/s320/IHaveWhoHas-Equations.JPG" width="320" /></a>An&nbsp;<b>I Have, Who Has</b>&nbsp;game is not a new concept. The premiss is that each person gets a card that has two statements. One is the "I have" statement and the other is the "Who has" statement. In this case the "I have" statement is a simple equation "Who has" statement which is the answer. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has 7?". Someone else will have a card where their equation has an answer that equals 7&nbsp;so they would say " I have 2x = 14". Who has negative 4?" That is,&nbsp;they read their equation that has an answer that equals 7&nbsp;and then asks their "Who has" statement. Then someone else will have an equation that matches -4 and the game continues. If done&nbsp;correctly, it should end up with the person who started giving their "I have" statement. It works really well as a warm up and one of nice things about this is that you could do it multiple days and kids will likely get different cards.<br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><ul><li>Gr7PA - solve linear equations of the form ax <span class="s1">= </span>c or c <span class="s1">= </span>ax and ax + b <span class="s1">= </span>c or variations such as b + ax <span class="s1">= </span>c and c <span class="s1">= </span>bx + a (where a, b, and c are natural numbers) by modelling with concrete materials, by inspection, or by guess and check, with and without the aid of a calculator&nbsp;<b>NOTE - only use the 9 card set if doing this for grade 7 as there are a few multi step equations;</b></li><li>Gr8PA - solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection, guess and check, and a “balance” model&nbsp;</li><li>MPM1D, MFM1P - solve first-degree equations, including equations with fractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies);</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><a href="http://3.bp.blogspot.com/-nAfZ-T5I-oQ/VnQCewOQsiI/AAAAAAAAGWw/Y4PB0dmaRyE/s1600/IHaveWhoHasEquations.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-nAfZ-T5I-oQ/VnQCewOQsiI/AAAAAAAAGWw/Y4PB0dmaRyE/s320/IHaveWhoHasEquations.png" width="239" /></a><li>There are two sets of cards that you could download here. One set (pictured here) has only 9 cards in it (you can see that the card on the top left has the "I have" to match the "Who has" of the card on the bottom right). Depending on the size of class you have you might want to use this set multiple times (ie groups of 9) or use the larger set of 27. Either way, in order for the game to work, all cards need to be passed out. So some students may need to have more than one card.</li><li>Regardless. Print out the set you want (ideally on coloured card stock) and we also suggest lamination to lengthen the lifespan of the cards.</li><li>Be sure to print out a set for yourself that you don't cut out so that it will be easier for you to check as students play the game.</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><ol><li>Distribute the cards one per student. All cards must be handed out so some students might need more than one card.</li><li>Tell each person to solve their "I have" equation and check their answer with at least one other person.&nbsp;</li><li>Once students are confident with their answer all students should stand and then you choose one to read their "Who has" statement. The person who's equation has the same answer should read their "I have" statement followed by their "Who has" statement and then sit down. Eventually the last person standing should be the person who started.&nbsp;</li><li>A variation might be to have students walk to the front and stand next to the person who they were matched with and eventually form an entire loop around the class.</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul><li>IHaveWhoHas-Equations-9cards (<a href="https://drive.google.com/open?id=0B9algQOOR_bkdFdzSkc3MVJhbW8" target="_blank">pdf</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkLTh5MXZlTnlpLW8" target="_blank">doc</a>)</li><li>IHaveWhoHas-Equationss-27cards (<a href="https://drive.google.com/open?id=0B9algQOOR_bkMFBpWko2LXg2Y00" target="_blank">pdf</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkR3g3NTZFdGJKdjQ" target="_blank">doc</a>)</li><li>IHaveWhoHas-BlankTemplate (<a href="https://drive.google.com/open?id=0B9algQOOR_bkR21WZVB6YmpqaGM" target="_blank">doc</a>)</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.7900009155273px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-43148328196303780512015-12-16T12:49:00.000-05:002016-06-13T19:51:19.030-04:00Simplifying Expressions with Algebra Tiles Matching Cards<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://4.bp.blogspot.com/-EXEx2Hv4luE/VnGbU4TbKgI/AAAAAAAAAw4/27K06ns6fOY/s1600/AlgebraTiles.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-EXEx2Hv4luE/VnGbU4TbKgI/AAAAAAAAAw4/27K06ns6fOY/s320/AlgebraTiles.JPG" width="320" /></a>This is a very simple matching activity where students are given a bunch of algebraic expressions (in one variable) and simplified expressions (both in algebraic and algebra tile form) and all they have to do is match up each expression with their simplified form. This is not meant to be a long or complex activity and could best be used as a warm up or end of class review or possibly just in the middle of a long class to switch up the period.<br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><ul><li>MPM1D - add and subtract polynomials with up to two variables [e.g., (2x – 5) + (3x + 1), (3x<sup>2</sup>y + 2xy<sup>2</sup>) + (4x<sup>2</sup>y – 6xy<sup>2</sup>)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);</li><li>MFM1P - add and subtract polynomials involving the same variable up to degree three [e.g., (2x + 1) + (x<sup>2</sup>– 3x + 4)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><a href="http://1.bp.blogspot.com/-PKvLKEuFQ24/VnGbtRDhfWI/AAAAAAAAAxA/8_yakzVeu04/s1600/Algebra%2BTiles.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-PKvLKEuFQ24/VnGbtRDhfWI/AAAAAAAAAxA/8_yakzVeu04/s320/Algebra%2BTiles.png" width="278" /></a><li>There are four sets of cards (each group would get a set so they aren't all working on the same questions). Each set of cards will have answers that have the same characteristics (Set 1 - answer is a trinomial, Set 2 - answer is a binomial with no squared term, Set 3 answer is a binomial with no x term, Set 4 - answer is a binomial with no constant term). A set should contain 12 cards. Four long expressions, four algebraic answers and four algebra tile answers.</li><li>Print and cut out the cards (we suggest laminating them to). Note that each card has what set number it belongs to so that if you mix them up you can easily sort them back into their sets. You may wish to put each set in an envelope or ziplock bag for easy distribution.</li><li>You will probably want to have physical algebra tiles for students to use while doing the actual simplification.</li><li>Note that because there doesn't seem to be a consensus on which colour algebra tiles represent positive or negative, there are two sets. One that assumes red is positive and one that assumes red is negative. Keep which ever is the protocol for your class and discard the other.</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><br /><ol><li>Students could be put into groups or do this individually. Ether way, since there are only four sets you will need to have multiple copies of each set.&nbsp;</li><li>Give each group an envelop and tiles and ask them to match the unsimplified expression with the simplified expression and algebra tile representation.&nbsp;</li><li>Once each group is done, have groups switch their envelopes. (1 gives to 2, 2 gives to 3 etc). You can do this 4 times.&nbsp;</li></ol><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><br /><ul><li>SimplifyingPolynomialsMatching (<a href="https://drive.google.com/open?id=0B9algQOOR_bkUkNNcHNzZ2YtLTA" target="_blank">pdf</a>, <a href="https://drive.google.com/open?id=0B9algQOOR_bkc0RHRWNNSWxyVW8" target="_blank">doc</a>)</li></ul><div><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span></div>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com1tag:blogger.com,1999:blog-7366940278418424797.post-11923356372316039152015-12-14T23:27:00.000-05:002015-12-18T09:30:23.494-05:00I Have, Who Has - Proportions<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://1.bp.blogspot.com/-OJL7rLtfxDY/Vm-IAr9FHgI/AAAAAAAAAv4/il8uegJeqnU/s1600/IHaveWhoHasProportions.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-OJL7rLtfxDY/Vm-IAr9FHgI/AAAAAAAAAv4/il8uegJeqnU/s320/IHaveWhoHasProportions.JPG" width="320" /></a>An&nbsp;<b>I Have, Who Has</b>&nbsp;game is not a new concept. The premiss is that each person gets a card that has two statements. One is the "I have" statement and the other is the "Who has" statement. In this case the "I have" statement is an proportion with a missing value and a "Who has" statement which is the answer. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has 24?". Someone else will have a card where their proportion has an answer that equals 24&nbsp;so they would say " I have 8 over x equals 5 over 15". Who has 56?" That is,&nbsp;they read their proportion that has an answer that equals 24&nbsp;and then asks their "Who has" statement. Then someone else will have an expression that matches 56&nbsp;and the game continues. If done&nbsp;correctly, it should end up with the person who started giving their "I have" statement. It works really well as a warm up and one of nice things about this is that you could do it multiple days and kids will likely get different cards.<br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><ul><li>Gr8PA - solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection, guess and check, and a “balance” model <b>NOTE - only use the 9 card set if doing this for grade 8; </b></li><li>MPM1D - solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion</li><li>MPM1D, MFM1P - solve first-degree equations, including equations with fractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies);</li><li><div class="p1">MFM1P - solve for the unknown value in a proportion, using a variety of methods</div></li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><a href="http://1.bp.blogspot.com/-0wEZSb1p6I8/Vm-UdhH_hrI/AAAAAAAAAwU/YFL4TQh9tb8/s1600/IHaveWhoHasProportions.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-0wEZSb1p6I8/Vm-UdhH_hrI/AAAAAAAAAwU/YFL4TQh9tb8/s320/IHaveWhoHasProportions.png" width="240" /></a><li>There are two sets of cards that you could download here. One set (pictured here) has only 9 cards in it (you can see that the card on the top left has the "I have" to match the "Who has" of the card on the bottom right). Depending on the size of class you have you might want to use this set multiple times (ie groups of 9) or use the larger set of 27. Either way, in order for the game to work, all cards need to be passed out. So some students may need to have more than one card.</li><li>Regardless. Print out the set you want (ideally on coloured card stock) and we also suggest lamination to lengthen the lifespan of the cards.</li><li>Be sure to print out a set for yourself that you don't cut out so that it will be easier for you to check as students play the game.</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><ol><li>Distribute the cards one per student. All cards must be handed out so some students might need more than one card.</li><li>Tell each person to answer their "I have" proportion and check their answer with at least one other person.&nbsp;</li><li>Once students are confident with their answer all students should stand and then you choose one to read their "Who has" statement. The person who's answer is the same should read their "I have" statement followed by their "Who has" statement and then sit down. Eventually the last person standing should be the person who started.&nbsp;</li><li>A variation might be to have students walk to the front and stand next to the person who they were matched with and eventually form an entire loop around the class.</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul><li>IHaveWhoHas-Proportions-9cards (<a href="https://drive.google.com/open?id=0B9algQOOR_bkTFliaUVjZGZRUkU" target="_blank">pdf</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkaXVVQzRPS1RSMTQ" target="_blank">doc</a>)</li><li>IHaveWhoHas-Proportions-27cards (<a href="https://drive.google.com/open?id=0B9algQOOR_bkUkhUclV0d1g3N2s" target="_blank">pdf</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkdkVCb2R2U2VxTE0" target="_blank">doc</a>)</li><li>IHaveWhoHas-BlankTemplate (<a href="https://drive.google.com/open?id=0B9algQOOR_bkR21WZVB6YmpqaGM" target="_blank">doc</a>)</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.7900009155273px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-57480988750177333712015-12-14T09:35:00.000-05:002015-12-18T09:31:37.995-05:00I Have, Who Has - Angles<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://2.bp.blogspot.com/-bwTLwlJuZW0/Vm691z1IFxI/AAAAAAAAAvU/Oda-lF1sjo8/s1600/IHaveWhoHasAngles.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-bwTLwlJuZW0/Vm691z1IFxI/AAAAAAAAAvU/Oda-lF1sjo8/s320/IHaveWhoHasAngles.JPG" width="320" /></a>An&nbsp;<b>I Have, Who Has</b>&nbsp;game is not a new concept. The premiss is that each person gets a card that has two statements. One is the "I have" statement and the other is the "Who has" statement. In this case the "I have" statement is an diagram dealing with determining an angle and a "Who has" statement which is the angle. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has 138<sup>o</sup>?". Someone else will have a card where their diagram has an angle that equals 138<sup>o</sup>&nbsp;so they would say " I have x = 138<sup>o</sup>". Who has&nbsp;136<sup>o</sup>?" That is,&nbsp;they read their angle that equals 138<sup>o</sup>&nbsp;and then asks their "Who has" statement. Then someone else will have an expression that matches&nbsp;136<sup>o</sup>&nbsp;and the game continues. If done&nbsp;correctly, it should end up with the person who started giving their "I have" statement. It works really well as a warm up and one of nice things about this is that you could do it multiple days and kids will likely get different cards.<br />In this set there are questions for parallel lines with a transversal, complimentary angles, supplementary angles, exterior angles, sum of interior angles and opposite angles questions<br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><ul><li>Gr8GSS - solve angle-relationship problems involving triangles (e.g., finding interior angles <div class="p1">or complementary angles), intersecting lines (e.g., finding supplementary angles or opposite angles), and parallel lines and transversals (e.g., finding alternate angles or corresponding angles) <b>NOTE - only use the 9 card set if doing this for grade 8;</b></div></li><li>MPM1D - determine, through investigation using a variety of tools (e.g., dynamic geometry software, paper folding), and describe some properties of polygons, and apply the results in problem solving</li><li>MPM1D, MFM1P - determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons</li><li><div class="p1">MFM1P - determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the angles formed by parallel lines cut by a transversal, and apply the results to problems involving parallel lines</div></li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><a href="http://1.bp.blogspot.com/-MYmRUXwnJKw/Vm7SWogt3sI/AAAAAAAAAvo/kNtoIzoJvpQ/s1600/IHaveWhoHasAngles.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://1.bp.blogspot.com/-MYmRUXwnJKw/Vm7SWogt3sI/AAAAAAAAAvo/kNtoIzoJvpQ/s200/IHaveWhoHasAngles.png" width="150" /></a><li>There are two sets of cards that you could download here. One set (pictured here) has only 9 cards in it (you can see that the card on the top left has the "I have" to match the "Who has" of the card on the bottom right). Depending on the size of class you have you might want to use this set multiple times (ie groups of 9) or use the larger set of 27. Either way, in order for the game to work, all cards need to be passed out. So some students may need to have more than one card.</li><li>Regardless. Print out the set you want (ideally on coloured card stock) and we also suggest lamination to lengthen the lifespan of the cards.</li><li>Be sure to print out a set for yourself that you don't cut out so that it will be easier for you to check as students play the game.</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><ol><li>Distribute the cards one per student. All cards must be handed out so some students might need more than one card.</li><li>Tell each person to determine the indicated angle in their "I have" diagram and check their answer with at least one other person.&nbsp;</li><li>Once students are confident with their answer all students should stand and then you choose one to read their "Who has" statement. The person who's answer is the same should read their "I have" statement followed by their "Who has" statement and then sit down. Eventually the last person standing should be the person who started.&nbsp;</li><li>A variation might be to have students walk to the front and stand next to the person who they were matched with and eventually form an entire loop around the class.</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul><li>IHaveWhoHas-Angles-9cards (<a href="https://drive.google.com/open?id=0B9algQOOR_bkOXNPcDIwNUh4V0E" target="_blank">pdf</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkVkJTWW9FWWxiRFk" target="_blank">doc</a>)</li><li>IHaveWhoHas-Angles-27cards (<a href="https://drive.google.com/open?id=0B9algQOOR_bkZkRwU1pnWTNKTlU" target="_blank">pdf</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkenhLM0VjTko2SDA" target="_blank">doc</a>)</li><li>IHaveWhoHas-BlankTemplate (<a href="https://drive.google.com/open?id=0B9algQOOR_bkR21WZVB6YmpqaGM" target="_blank">doc</a>)</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.7900009155273px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-32321844607087122042015-12-13T23:57:00.001-05:002015-12-14T23:24:05.934-05:00I Have, Who Has - Simplifying Expression<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://2.bp.blogspot.com/-g-9E1rGg6sE/Vm5G4hxrzzI/AAAAAAAAAu8/uuYyDC5Vys4/s1600/IHaveWhoHasSimplifying.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-g-9E1rGg6sE/Vm5G4hxrzzI/AAAAAAAAAu8/uuYyDC5Vys4/s320/IHaveWhoHasSimplifying.JPG" width="320" /></a>An <b>I Have, Who Has</b> game is not a new concept. The premiss is that each person gets a card that has two statements. One is the "I have" statement and the other is the "Who has" statement. In this case the "I have" statement is an expression dealing with a polynomial and a "Who has" statement which is the simplified form. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has -3d<sup>2</sup>?". Someone else will have a card where their expression equals -3d<sup>2</sup> so they would say " I have 4d<sup>2</sup> - 9d<sup>2</sup> - d<sup>2</sup> + 3d<sup>2</sup>". Who has 3x + 2y?" That is, they read their expression that equals -3d<sup>2</sup> and then asks their "Who has" statement. Then someone else will have an expression that matches 3x + 2y&nbsp;and the game continues. If done correctly, it should end up with the person who started giving their "I have" statement. It works really well as a warm up and one of nice things about this is that you could do it multiple days and kids will likely get different cards.<br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><ul><li>MPM1D - add and subtract polynomials with up to two variables, using a variety of tools</li><li>MFM1P - add and subtract polynomials involving the same variable up to degree three, using a variety&nbsp;of tools&nbsp;</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><a href="http://4.bp.blogspot.com/-fQwOhWnmnWQ/Vm5HO6ZZeyI/AAAAAAAAAvE/QIkTQ9Jx2HE/s1600/IHaveWhoHasSimplifying.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://4.bp.blogspot.com/-fQwOhWnmnWQ/Vm5HO6ZZeyI/AAAAAAAAAvE/QIkTQ9Jx2HE/s200/IHaveWhoHasSimplifying.png" width="151" /></a><li>There are two sets of cards that you could download here. One set (pictured here) has only 9 cards in it (you can see that the card on the top left has the "I have" to match the "Who has" of the card on the bottom right). Depending on the size of class you have you might want to use this set multiple times (ie groups of 9) or use the larger set of 27. Either way, in order for the game to work, all cards need to be passed out. So some students may need to have more than one card.</li><li>Regardless. Print out the set you want (ideally on coloured card stock) and we also suggest lamination to lengthen the lifespan of the cards.</li><li>Be sure to print out a set for yourself that you don't cut out so that it will be easier for you to check as students play the game.</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><ol><li>Distribute the cards one per student. All cards must be handed out so some students might need more than one card.</li><li>Tell each person to simplify their "I have" expression and check their answer with at least one other person.&nbsp;</li><li>Once students are confident with their simplification all students should stand and then you choose one to read their "Who has" statement. The person who's simplified answer is the same should read their "I have" statement followed by their "Who has" statement and then sit down. Eventually the last person standing should be the person who started.&nbsp;</li><li>A variation might be to have students walk to the front and stand next to the person who they were matched with and eventually form an entire loop around the class.</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul><li>IHaveWhoHas-Simplifying-9cards (<a href="https://drive.google.com/open?id=0B9algQOOR_bkRVJNaXZwUjVqWGM" target="_blank">pdf</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkT0xZdzA2enNtLUU" target="_blank">doc</a>)</li><li>IHaveWhoHas-Simplifying-27cards (<a href="https://drive.google.com/open?id=0B9algQOOR_bkMFRMbVlMU1VnMkE" target="_blank">pdf</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkS3Z0RmNVWi1pZFk" target="_blank">doc</a>)</li><li>IHaveWhoHas-BlankTemplate (<a href="https://drive.google.com/open?id=0B9algQOOR_bkR21WZVB6YmpqaGM" target="_blank">doc</a>)</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.7900009155273px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-78494950889159856492015-10-20T12:37:00.000-04:002015-10-23T12:13:45.097-04:00Polygraph - Distance Time Graphs<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://www.iytgames.com/uploads/2/5/7/2/25721284/s366773919327452515_p22_i1_w2560.jpeg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://www.iytgames.com/uploads/2/5/7/2/25721284/s366773919327452515_p22_i1_w2560.jpeg" height="143" width="200" /></a>Have you ever played the game "Guess Who?". In that game you have a grid of people to look at and you choose one. Your partner has the same grid and gets to ask you yes or no<br /><a href="http://3.bp.blogspot.com/-aBAbsXh_Ro8/Vipcon-9QmI/AAAAAAAAGL0/nrQs3ADj3tY/s1600/PolyGraph%2BD-T.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-aBAbsXh_Ro8/Vipcon-9QmI/AAAAAAAAGL0/nrQs3ADj3tY/s320/PolyGraph%2BD-T.png" width="320" /></a>questions. As they ask questions and get their answers they start to eliminate people until they have only one left. Well the crew at Desmos have created a gave called <a href="http://blog.desmos.com/post/105283812542/polygraph" target="_blank">Polygraph</a> that works the same way except for graphs (and other topics). So far they have created one for&nbsp;<a href="https://teacher.desmos.com/polygraph-parabolas" target="_blank">parabolas</a>,&nbsp;<a href="https://teacher.desmos.com/polygraph-lines" target="_blank">lines</a>,&nbsp;<a href="https://teacher.desmos.com/polygraph-rationals" target="_blank">rational functions</a>,&nbsp;<a href="https://teacher.desmos.com/polygraph-basic-quad" target="_blank">quadrilaterals</a>,&nbsp;<a href="https://teacher.desmos.com/polygraph-adv-quad" target="_blank">advanced quadrilaterals</a>&nbsp;and&nbsp;<a href="https://teacher.desmos.com/polygraph-hexagons" target="_blank">hexagons</a>. The way it works is you start a new session and get the 4 character code. Your students then go to&nbsp;&nbsp;<a href="http://student.desmos.com/">student.desmos.com</a>&nbsp;and enter that code. They will the get a brief (optional) training session on how to play the game and then the software will randomly select students to play against each other, taking turns as to who asks and answers the questions.<br /><br />But that is not the best part. The best part is they have created the <a href="http://blog.desmos.com/post/122854798480/polygraph-custom-edition" target="_blank">Polygraph editor</a> so anyone can create their own Polygraph. So that is what we did. This one is about the characteristics of a <a href="https://teacher.desmos.com/polygraph/custom/56251492a23c2d7208dfe072" target="_blank">Distance-Time graph</a> (or more generally a piecewise linear graph). There are no scales on these graphs so students will have to use general terms but we still think they will be able to relate to these with appropriate questions.<br /><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><div class="p1"></div><ul><li>MFM1P, MPM1D - describe a situation that would explain the events illustrated by a given graph of a relationship between two variables&nbsp;</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><li>Each student needs their own device connected to the internet. A phone will work but the images will be small. You may want to group kids together if the number of devices is limited.&nbsp;</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><ol><a href="http://3.bp.blogspot.com/-eiwAQutQZqA/ViZwSXD6XNI/AAAAAAAAAsM/dD0A45ijetw/s1600/Polygraph%2B-%2BStudents.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://3.bp.blogspot.com/-eiwAQutQZqA/ViZwSXD6XNI/AAAAAAAAAsM/dD0A45ijetw/s200/Polygraph%2B-%2BStudents.png" width="190" /></a><li>Go to&nbsp;<a href="https://teacher.desmos.com/polygraph/custom/56251492a23c2d7208dfe072" target="_blank">this link</a>&nbsp;and click on Start a New Session. You will have to log in to start a session but you can do that with your Google account or create your own. This will keep track of how your students responded and you can look at this any time you wish. You will be give a 4 character code that your students type in at <a href="http://student.desmos.com/">student.desmos.com</a>.</li><li>Once students log in they will try a test round with faces (they can skip this once they know what to do) and then as students complete the test round they will be paired up automatically with other students who have finished the test round.&nbsp;</li><li>Instruct students to ask questions as if they were distance-time graphs&nbsp;</li><li>Circulate through your class if there are questions.&nbsp;</li><li>Note that you will need an even number of players otherwise there will be always someone sitting out.</li></ol><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div>No downloads needed, just the link&nbsp;<a href="https://teacher.desmos.com/polygraph/custom/56251492a23c2d7208dfe072" target="_blank">https://teacher.desmos.com/polygraph/custom/56251492a23c2d7208dfe072</a><br /><br /><span style="background-color: white; color: #6a6a6a; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15.5556px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-35480959866508702602015-10-16T13:44:00.000-04:002016-03-21T23:04:45.396-04:00Geometer's Sketchpad - Combining Velocity Vectors<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://4.bp.blogspot.com/-tEiBmxSyMhY/ViEwTSPFCHI/AAAAAAAAArs/IIlFNOLvu5U/s1600/GSP-vectorcircle.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="237" src="https://4.bp.blogspot.com/-tEiBmxSyMhY/ViEwTSPFCHI/AAAAAAAAArs/IIlFNOLvu5U/s320/GSP-vectorcircle.png" width="320" /></a><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;">When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).</span><br /><span style="color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif;"><span style="background-color: white; font-size: 14.85px; line-height: 20.79px;">In this activity, students will walk through a demonstration of how the combination of two linear motions can create a complex two dimensional motion (in this case circular motion). Some things that I think are important here are the fact that the two motions are completely independent of each other and the idea of how the look of a velocity vector changes as you speed up and slow down. The sketch is meant for students to walk through and answer questions as they go. You could also use it in the calculus part of the course to talk about velocity increasing/decreasing and what that looks like for motion.</span></span><br /><span style="color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif;"><span style="background-color: white; font-size: 14.85px; line-height: 20.79px;"><br /></span></span><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><div class="p1"></div><ul><li>A1.1 - describe examples of real-world applications of rates of change, represented in a variety of ways (e.g., in words, numerically, graphically, algebraically)</li><li>C1.2 - represent a vector in two-space geometrically as a directed line segment, with direction expressed in different ways (e.g., 320º; N 40º W), and algebraically (e.g., using Cartesian coordinates; using polar coordinates), and recognize vectors with the same magnitude and direction but different positions as equal vectors</li><li>C2.1 - perform the operations of addition, subtraction, and scalar multiplication on vectors represented as directed line segments in two space, and on vectors represented in Cartesian form in two-space and three-space</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul style="background-color: white; color: #6a6a6a; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px; margin: 0.5em 0px; padding: 0px 2.5em;"><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">All that is needed is the electronic download (below)</li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">Note that this really works well on an iPad using the&nbsp;<a href="https://itunes.apple.com/ca/app/sketchpad-explorer/id452811793?mt=8" style="color: #7ba2d3; text-decoration: none;" target="_blank">Sketchpad Explorer App</a>&nbsp;(which is free)</li><li>You can also use this on any web based computer (or Chromebook) with this&nbsp;<span style="color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;"><a href="http://mail.wecdsb.on.ca/~david_petro/WebSketches/CircleVector/index.html" target="_blank">Web&nbsp;sketch</a></span></li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div>Watch the video below to see how to use the sketch<br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/4nG0Kqtb_ko/0.jpg" frameborder="0" height="315" src="https://www.youtube.com/embed/4nG0Kqtb_ko?feature=player_embedded" width="530"></iframe></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul style="background-color: white; color: #6a6a6a; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px; margin: 0.5em 0px; padding: 0px 2.5em;"><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">CircleVector.gsp (<a href="http://mail.wecdsb.on.ca/~david_petro/sketches/CircleVectors.gsp" style="color: #7ba2d3; text-decoration: none;" target="_blank">iPad/V5</a>)</li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px;">Web&nbsp;sketch&nbsp;</span><a href="http://mail.wecdsb.on.ca/~david_petro/WebSketches/CircleVector/index.html" style="color: #7ba2d3; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px; text-decoration: none;" target="_blank">here</a></li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">For more sketches like this go to my&nbsp;<a href="http://mail.wecdsb.on.ca/~david_petro/sketches/Sketches.htm" style="color: #7ba2d3; text-decoration: none;" target="_blank">full page</a></li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15.5556px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-74982456103108712842015-10-15T16:02:00.000-04:002016-03-21T23:03:18.804-04:00Geometer's Sketchpad - Practice Line of Best Fit<div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://3.bp.blogspot.com/-WvijWr7NADI/ViAAWN448hI/AAAAAAAAArc/NoJzVvSaS5A/s1600/Line%2Bof%2BBest%2BFit.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="236" src="https://3.bp.blogspot.com/-WvijWr7NADI/ViAAWN448hI/AAAAAAAAArc/NoJzVvSaS5A/s320/Line%2Bof%2BBest%2BFit.png" width="320" /></a><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;">When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).</span><br /><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;">In this activity, students practice placing the line of best fit on a linear set of data. It's not meant to be really difficult but just to reenforce the idea of what the line of best fit is. Students can check their answer and try as many as they like. Clicking the Medium or Hard buttons will spread the points out more randomly to make the line a bit harder to determine. This is not meant to be really hard but just a quick way to determine if students have the basic concept of what a line of best fit is</span><br /><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;"><br /></span><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><ul><li>MPM1D, MFM1P - construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools (e.g., spreadsheets, graphing software, graphing calculators, paper and pencil), for linearly related and non-linearly related data collected from a variety of sources</li><li>MAP4C - D1.4 - create a graphical summary of two-variable data using a scatter plot (e.g., by identifying and justifying the dependent and independent variables; by drawing the line of best fit, when appropriate), with and without technology</li><li>MDM4U - D2.4 - generate, using technology, the relevant graphical summaries of two-variable data (e.g., scatter plots, side-by-side boxplots) based on the type of data provided (e.g., categorical, ordinal, quantitative)</li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul style="background-color: white; color: #6a6a6a; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px; margin: 0.5em 0px; padding: 0px 2.5em;"><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">All that is needed is the electronic download (below)</li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">Note that this really works well on an iPad using the&nbsp;<a href="https://itunes.apple.com/ca/app/sketchpad-explorer/id452811793?mt=8" style="color: #7ba2d3; text-decoration: none;" target="_blank">Sketchpad Explorer App</a>&nbsp;(which is free)</li><li>You can also use this on any web based computer (or Chromebook) with this&nbsp;<span style="color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 14.85px; line-height: 20.79px;"><a href="http://mail.wecdsb.on.ca/~david_petro/WebSketches/BestLine/index.html" target="_blank">Web&nbsp;sketch</a></span></li></ul><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div>Watch the video below to see how to use the sketch<br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/J8Zm45N4TMQ/0.jpg" frameborder="0" height="315" src="https://www.youtube.com/embed/J8Zm45N4TMQ?feature=player_embedded" width="530"></iframe></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="https://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul style="background-color: white; color: #6a6a6a; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px; margin: 0.5em 0px; padding: 0px 2.5em;"><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">Line of Best Fit.gsp (<a href="http://mail.wecdsb.on.ca/~david_petro/sketches/line%20of%20best%20fit.gsp" style="color: #7ba2d3; text-decoration: none;" target="_blank">iPad/V5</a>)</li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px;">Web&nbsp;sketch&nbsp;</span><a href="http://mail.wecdsb.on.ca/~david_petro/WebSketches/BestLine/index.html" style="color: #7ba2d3; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; line-height: 20.79px; text-decoration: none;" target="_blank">here</a></li><li style="border: none; margin: 0px 0px 0.25em; padding: 0px;">For more sketches like this go to my&nbsp;<a href="http://mail.wecdsb.on.ca/~david_petro/sketches/Sketches.htm" style="color: #7ba2d3; text-decoration: none;" target="_blank">full page</a></li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15.5556px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0tag:blogger.com,1999:blog-7366940278418424797.post-8661466298996004022015-09-21T11:48:00.000-04:002015-12-14T23:23:38.171-05:00I Have, Who Has - Making Change in Canada<div class="separator" style="clear: both;"><a href="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s1600/EM_Activity.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-E_4dNzZPm_M/U615nRGBanI/AAAAAAAAAFE/dvxm1BnUIEU/s320/EM_Activity.png" width="320" /></a></div><a href="http://1.bp.blogspot.com/-OM8g0fresUI/VgAeeyVvWFI/AAAAAAAAAqU/JH5r8TrGp8g/s1600/IHaveWhoHas-Change.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://1.bp.blogspot.com/-OM8g0fresUI/VgAeeyVvWFI/AAAAAAAAAqU/JH5r8TrGp8g/s200/IHaveWhoHas-Change.jpg" width="200" /></a>An I Have, Who Has game is not a new concept. The premiss is that each person gets a card that has two statements. One is the "I have" statement and the other is the "Who has" statement. In this case the "I have" statement is an expression dealing with making change with money in Canada. If you are not from Canada, you may not know that here <a href="http://www.mint.ca/store/mint/about-the-mint/phasing-out-the-penny-6900002#.VgAhSyBVikp" target="_blank">we no longer use pennies</a>. This means that when we buy things and pay cash we actually have to round to the nearest nickel to make change. The way the game works is that a person starts by reading their "Who has" statement. For example, someone might say "Who has $4.35?". Someone else will have a card where their change equals $4.35 so they would say "I have $20 and it costs $15.63. Who has change of $1.75?" That is, they read their statement that equals $4.35 and then asks their "Who has" statement. Then someone else will have an expression that matches $1.75 and the game continues. If done correctly, it should end up with the person who started giving their "I have" statement. It works really well as a warm up and one of nice things about this is that you could do it multiple days and kids will likely get different cards.<br /><br /><div class="separator" style="clear: both;"><a href="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s1600/EM_Curriculum.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://1.bp.blogspot.com/-jQBX4ggDjws/U615nXUhjoI/AAAAAAAAAEs/l8lYckakGMU/s320/EM_Curriculum.png" width="320" /></a></div><div class="separator" style="clear: both;"></div><ul><li>MAT1L - DMS1.03 – round money values to stated accuracies (e.g., the nearest cent, the nearest dollar, the nearest ten dollars, the nearest hundred dollars, the nearest thousand dollars, and the nearest million dollars), in applications drawn from everyday situations; DMS2.01 – make the correct change for an offered amount with and without concrete materials (e.g., change from a $5 bill for an item costing $4.77);</li><li>MAT2L - EMS1.01 – read and interpret money values given in words, write money values as decimals, and round money values appropriately, in solving problems found in everyday contexts;</li></ul><div class="separator" style="clear: both;"><a href="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s1600/EM_Materials.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://4.bp.blogspot.com/-08Ko_TEz4xo/U615oHk0LfI/AAAAAAAAAE0/GiERNLUWZyY/s320/EM_Materials.png" width="320" /></a></div><ul><a href="http://3.bp.blogspot.com/-eAxprL7a_Lk/VgAeemibNrI/AAAAAAAAAqI/P4VVt6N_SwI/s1600/IHaveWhoHas-Change.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://3.bp.blogspot.com/-eAxprL7a_Lk/VgAeemibNrI/AAAAAAAAAqI/P4VVt6N_SwI/s200/IHaveWhoHas-Change.png" width="147" /></a><li>This is a small set that has only 9 cards in it (you can see that the card on the top left has the "I have" to match the "Who has" of the card on the bottom right). You will likely have more than 9 students in your class and so will need multiple sets (ie groups of 9). In order for the game to work, all cards need to be passed out. So some students may need to have more than one card.</li><li>Print out the set you want (ideally on coloured card stock) and we also suggest lamination to lengthen the lifespan of the cards.</li><li>Be sure to print out a set for yourself that you don't cut out so that it will be easier for you to check as students play the game.</li></ul><div class="separator" style="clear: both;"><a href="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s1600/EM_Procedure.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-4jS2pXHL14I/U615oMrX6WI/AAAAAAAAAFA/aOkeQgg3-GU/s320/EM_Procedure.png" width="320" /></a></div><ol><a href="http://www.mint.ca/store/dyn/content_imgs/rounding2-e.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://www.mint.ca/store/dyn/content_imgs/rounding2-e.jpg" height="134" width="320" /></a><li>Make sure you have gone over the rounding rules for money first.&nbsp;</li><li>Distribute the cards one per student. All cards must be handed out so some students might need more than one card.</li><li>Tell each person to calculate the change for their "I have" expression and check their answer with at least one other person.&nbsp;</li><li>Once students are confident with their answers all students should stand in their groups and then you choose one to read their "Who has" statement. The person who's answer is the same should read their "I have" statement followed by their "Who has" statement and then sit down. Eventually the last person standing should be the person who started.&nbsp;</li><li>A variation might be to have students walk to the front and stand next to the person who they were matched with and eventually form an entire loop around the class.</li></ol><div class="separator" style="clear: both;"><a href="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s1600/EM_Downloads.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="33" src="http://2.bp.blogspot.com/-NZa7E3cjmhI/U615nWGLIbI/AAAAAAAAAFM/ocurrwbJZHM/s320/EM_Downloads.png" width="320" /></a></div><ul><li>IHaveWhoHas-MakingChange (<a href="https://drive.google.com/open?id=0B9algQOOR_bkUXNzQnFhU3lGSTg" target="_blank">pdf</a>) (<a href="https://drive.google.com/open?id=0B9algQOOR_bkUU9vdXNGZVk0MUE" target="_blank">doc</a>)</li><li>IHaveWhoHas-BlankTemplate (<a href="https://drive.google.com/open?id=0B9algQOOR_bkR21WZVB6YmpqaGM" target="_blank">doc</a>)</li></ul><span style="background-color: white; color: #6a6a6a; font-family: &quot;arial&quot; , &quot;tahoma&quot; , &quot;helvetica&quot; , &quot;freesans&quot; , sans-serif; font-size: 15px; line-height: 20.79px;">Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks</span>David Petrohttps://plus.google.com/106463796285240605969noreply@blogger.com0